Since F is an isomorphism by assumption, it is onto and a. Answer of 1. If Ker0 # F, show that R has no zero divisors. There is no set of all homomorphisms, so there’s no way to define the size. How many elements of order 6 are there in Z 6 Z 9? The order of (a;b) is the least common multiple of the order of aand that of b. Calculate all of the elements in 2 2. Q: Consider the subset ℚ(sqrt3) = {a + b : a, b ∈ ℚ} of ℝ. Determine 4, imy and ker y. How many homomorphisms are there from Z20 onto Z,? How many are there to Z ?. 8k 13. Question: 14. $1)$ If $\phi$$(1)=a$, then $|a|$ should divide both, order of the field as well as the order of the ring. There are two possibilities , and ,. Thus possible homomorphisms are of the form x → 2i · x where i = 0,1,2,3. There is evidence that computational problems involving surjective homomorphisms are more difficult than those involving (unrestricted) homomorphisms. if ker(φ) = {e}, φ must be injective, which would imply S3 and Z6 were isomorphic. So φ(k) = 0 ∈Z 12 if and only if k ∈{0,6,12}⊂Z 18. Macauley (Clemson) Lecture 4. Since f is a function and Z m is finite, f being onto Z m forces f to be 1-1. Exercise 13. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Elements Of Modern Algebra. Question: (a) Show that there are no surjective homomorphisms from Z20 to Zg. ) - Pedro ♦. (2) Let G = Z under addition and G = {1, 1} under multiplication. Any help would be. To have a map from. MathAlgebraHow many homomorphisms are there from Z20 onto Z10? How manyare there. Please advice on onto and one -one part of this proof. Proof: This follows because φ is an additive group homomorphism, and Z is free on { 1 }. We say x ∈ R x ∈ R is a unit if xy = 1 x y = 1 for some y ∈ R y ∈ R. # 25: How many homomorphisms are there from Z20 onto Z10 ? How many are there to Z10 ? Again, the difference here is onto. f is Epimorphism, if f is surjective (onto). First consider the image of ϕ, which must be a subgroup of A ≅ C 2. a) A homomorphism f: Z6 → Z3 is defined by its value f (1) on the generator. We would like to show you a description here but the site won't allow us. We conclude by noting that $\frac{48+24}{\phi(10)}= \frac{72}{4} = 18$ cyclic subgroups of order 10. That's not to say that there isn't a homomorphism ˚: Z 3!Z 4; note that there is always thetrivial homomorphismbetween two groups: ˚: G ! H ; ˚(g) = 1 H for all g 2G : Exercise Show that there is no embedding ˚: Z n,!Z, for n 2. Show your reasoning (b) How many homomorphisms are there from Zso to Zio. Remember also that for a group homomorphism ˚: G!G0it's always true that ˚(e) = e0. A homomorphism is a map between two groups which respects the group structure. Therefore, the number of surjective homomorphisms is 2 * 2 * 2 = 8. Thus the quotient group G/ker (Φ) is well-defined. the only ring homomorphisms from Z to Z are the zero map and the identity map. (a) Explain why x 7→ 3x from Z12 to Z10 is not a homomorphism. How many homomorphisms are there from Z20 onto Z ? How many are there to Z ? weit wide C2C Ald. The normalizeris generated by (12345) and (15)(24), it has 10 elements and one can check that it is isomorphic to D5. Aside: there are only five non-isomorphic groups of order 12; what is the other one? Not an easy question to answer. That is, functions for which it doesn't matter whether we perform our group operation before or after applying the function. Answer to Solved Find all possible ring homomorphisms q: Z10 Z20. Edit : We use 2 properties of homomorphism: P1)Homomorphic image of idempotent is idempotent. There is no homomorpphism from Z 20 onto Z 8. If ker(f) = S4 there is only 1 homomorphism. Advanced Math questions and answers. if H and K are subgroups of a group G then H ∪ K is may or maynot be a subgroup. I try to break each. Recall the biholomorphic map G(w) = i1−w 1+w from D to H we introduced in Equation 2. Fundamental their of cyclic groups and U (10). Then number of homomorphism φ:Z5 to Z20. 8, ’ 1(h2i) and ’ (h5i) are normal subgroups of G(since h2iand h5iare normal subgroups of Z 10). A homomorphism his said to use an edge {v1,v2} ∈ E(H) if there is is an edge {u1,u2} ∈ E(G) such that. Case 1(H ˘=Z 4): Then G ˘=Z5 of Z 4. Q: How many homomorphisms are there from Z20 onto Z10? How manyare there to Z10? How manyare there to Z10? A: To find: Number of homomorphisms from Z20 onto Z10 and the number of homomorphisms to Z10. There are homomorphisms from Z20toZ8 that are not onto. Since F is an isomorphism by assumption, it is onto and a. There is no set of all homomorphisms, so there’s no way to define the size. Solution: Let x,y∈ G, then γφ(xy) = γ(φ(xy)) = γ(φ(x)φ(y)) = γφ(x)γφ(y) So γφsatisfies the homomorphism property. For the second, use. Hence the three groups Z2 ×Z2 ×Z2, Z2 ×Z4 and Z8 are not isomorphic, by Theorem 41(d). Macauley (Clemson) Chapter 8: Homomorphisms Math 4120, Spring 2014 10 / 50. Consequently, we see that $\phi(1)$ determines $\phi$ for any homomorphism $\phi$, and there are only six choices for this element, therefore there are at most six homomorphisms. If φ : Z20 → Z8 is a homomorphism then the order of φ(1) divides gcd(8,20) = 4 so φ(1) is in a unique subgroup of order 4 which is 2Z8. Let G be a finite group. The paper should be double space and properly. na ≡ 0 mod m and a ≡ a2 mod m. There is no homomorpphism from Z 20 onto Z 8. If g(x) = axis a ring homomorphism, then it is a group homomorphism and na 0 mod m. For Notes and Practice set WhatsApp @ 8130648819 or visit our Websitehttps://www. (i) Determine all homomorphisms from Z18 to Z24. Also a ≡ g(1) ≡ g(12) ≡ g(1)2 ≡ a2 mod m. Then either g= eor ghas order 2, so by assump-tion we must have g= e. certain kinds of functions between groups. Solutions for Chapter 10 Problem 20E: How many homomorphisms are there from Z20 onto Z8? How many are there to Z8?. $$ I know that the GDC of both groups gives me the number of existing homomorphisms. Holley EFI 300-719BK Holley 300-719BK Holley. Ran great at first, but only briefly. (a) How many homomorphisms ϕ:F3→D5 are there? (b) How many surjective homomorphisms ϕ:F3→Z5 are there? (c) (Bonus - not for assessment. It follows that a 1k 1 = b 1k 2. That's not to say that there isn't a homomorphism ˚: Z 3!Z 4; note that there is always thetrivial homomorphismbetween two groups: ˚: G ! H ; ˚(g) = 1 H for all g 2G : Exercise Show that there is no embedding ˚: Z n,!Z, for n 2. How many elements of order 6 are there in Z 6 Z 9? The order of (a;b) is the least common multiple of the order of aand that of b. I am asked to find all group homomorphisms from Z/4Z Z / 4 Z to Z/6Z Z / 6 Z. l= ka 1b 1 = ab 1 = a 1b. (The factorial terms disappear here, because we are counting homomorphisms rather than copies). Any of the 4 non-zero members of ZZ_5 are possible, since they are all of order 5 and generate ZZ_5. How many homomorphisms are there from Z20 onto Z8 how many homomorphisms are there from Z20 to Z8? There is no homomorpphism from Z20 onto Z8. then determine whether is one-to-one or onto. There are two distinct homomorphisms from $\mathbb{Z}$ to $\mathbb{Z}_2$, for example: The zero map, and the map sending $1_{\mathbb{Z}}$ to $1_{\mathbb{Z}_2}$. Pure maths with Usama. com/santoshifamilyJoin this channel to get access to perks:https:/. Then a is invertible in Z m and there is some b in Zm such that b a = 1. Suppose that I'm interested in finding all group homomorphisms from $\mathbb{Z}_7$ to $\mathbb{Z}_{12}$. Suppose that ˚is a homomorphism from Z 30 to Z 30 and that Ker(˚) = f0;10;20g. Also if I drop this unital homomorphism are there others? abstract-algebra; ring-theory; Share. And 11 ⋅ 11 = 121 = 1 11. On the one hand, we have φ(0) = 0, by Theorem 13. There is no homomorpphism from Z 20 onto Z 8. : D S is a homomorphism. If you are looking to construct an isomorphism between the two groups why not start by listing the elements of Z2 ×Z3 Z 2 × Z 3 and figuring out if any of them have order 6 6? If you can find one then it generates a cyclic subgroup of order 6 6 (a subgroup isomorphic to Z6 Z 6) inside your group of order 6 6. (a) How many homomorphisms are there from Z20 onto Z10? How many are there to Zio? Justify your answer. where G = Z and H = Z2 = Z/2Z is the standard group of order two, by the rule. Define a map ψ: Z → ker(ϕ) by sending k ∈ Z to mk + nZ. A homomorphism that is. φ(xy) = φ(x)φ(y) φ ( x y) = φ ( x) φ ( y) ). (b) Z 9 Z 9 and Z 27 Z 3. A homomorphism ϕ from Z20 to Z16 is completely determined by specifying where the image of the generator z of z ≅Z20 maps to. The cyclic subgroup generated by 2 is 2 = {0, 2, 4}. This homomorphism is injective (or one. Pure maths with Usama 3. Thus, the total number is 5. Also a ≡ g(1) ≡ g(12) ≡ g(1)2 ≡ a2 mod m. We now look at Groups as structures. Which of these are valid? Note that we must have ϕ ( x) 20 = 1 and ϕ ( x) 8 = 1. , ker˚= f(0;0)g. Maybe bromo Online 10 | Group Homomorphisms 221 G 22 homme 24 ma 25. I argue there are exactly two homomorphisms from Z to Z: the trivial map f (a) = 1 and the identity map f (a) = a, and thus that there is only one onto homomorphism from Z to Z. Define a map. Expert Answer. Define a map. Thus, S 4 6˘= D 12. Determine all homomorphisms from Z12 to Z20. How many homomorphisms are there from Z20 onto Z10? How many are there to Z10 ?. Homomorphisms between fields are injective. Solutions for Chapter 10 Problem 25EX: How many homomorphisms are there from Z20 onto Z10? How many are there to Z10? Get solutions Get solutions Get solutions done loading Looking for the textbook?. There is no homomorpphism from Z20onto Z8. It follows that there are four ring homomorphisms which are given by $f_1 (1) = (0, 0)$, $f_2 (1) = (1, 0)$, $f_3 (1) = (0, 1)$, $f_4 (1) = (1, 1)$. 2: Homomorphism Let G and H be groups, and ϕ: G → H. 2: Homomorphism Let G and H be groups, and ϕ: G → H. This means there are exactly three homomorphisms $\mathbb Z_{15} \to \mathbb Z_{18}$. Add to solve later. Login; Sign up; Textbooks; Ask our Educators;. Suppose that f is a homomorphism from S 4 onto Z 2. All homomorphisms coming from Z20 Z 20 are entirely determined by where they send 1. De nition: f is called one-to-one if f (x 1) = f (x 2) )x 1 = x 2:. is "infinite number of homomorphisms". This amounts to ϕ(z20) = ϕ(z)20 being trivial. The Sylow theorems imply that G has a normal subgroup N of order 5 and a complementary subgroup H of order 4. It means that for any g′ ∈ G′ we have some g ∈ G such that Φ (g)=g′. Edit: It is easy to show that any ring homomorphism ϕ: Zn → Zm ϕ: Z n → Z m is determined completely by the value of ϕ(1) ϕ ( 1). In group theory, two groups are said to be isomorphic if there exists a bijective homomorphism (also called an isomorphism) between them. Familiar homomorphisms. Let G be a finite group. (a) How many homomorphisms ϕ:F3→D5 are there? (b) How many surjective homomorphisms ϕ:F3→Z5 are there?. Holley EFI 300-719BK Holley 300-719BK Holley. Now, let's examine homomorphisms to Z10. Group Homomorphisms; Problems; Problem no. Let them be H2 and H3 respectively. How many homomorphisms are there from Z20 to Z8? How many of them are onto?. So the answer is: there are 1 + 9 + 6 = 16 1 + 9 + 6 = 16 elements of order 1, 2 or 4 in S4 S 4, hence 16 homomorphisms from Z4 Z 4 into S4 S 4. However, I'm confused about how to find out how many of these homomorphisms are onto. Also a ≡ g(1) ≡ g(12) ≡ g(1)2 ≡ a2 mod m. (ii) Suppose o : Z20 → Z10 is a homomorphism with $ (7) = 4. The first two properties stipulate that f should "preserve" the ring structure — addition and multipli-cation. As an example one can take a subgroup generated by (12345). Definition 2. View this answer View a sample solution. Then there exists r 1,r 2 ∈ R such that φ(r 1) = s 1 and φ(r 2) = s 2. Maybe bromo Online 10 | Group Homomorphisms 221 G 22 homme 24 ma 25. Find the kernel Kof φ. All other choices are allowed because they all commute. Holley EFI 300-719BK Holley 300-719BK Holley. Unfortunately, one then has . Log On Test Calculators and Practice Test. 12: Since 12 does not divide 63, there are $\boxed{0}$ group homomorphisms with an image of size 12. Determine 4, imy and ker y. For 'to be nontrivial, Aneeds to have order 3, and there are two choices for that. So there are 4 homomorphisms onto Z10. 1, above. 117k 7 71 167. Solution: Call this map. 4 Ring Homomorphisms and Group Rings. 2: Homomorphism Let G and H be groups, and ϕ: G → H. (a) How many graph homomorphisms are there from an edgeless graph to a graph with. 11 Direct Products, Finitely Generated Abelian Groups 3 Note. Is a ring homomorphism a group homomorphism? φ(a + b) = φ(a) + φ(b) • φ(ab) = φ(a)φ(b) Note that the operations may in theory differ, the left being in R and the right in S. So there are 4 homomorphisms onto Z10. The above map θ is an example of onto homomorphism. The exact question in the book is "Determine the number of homomorphisms from the additive group Z15 to the additive group Z10" (Zn is cyclic group of integers mod n under addition) Now if the question asks to find the number of homomorphisms from Z15 onto Z10, then by the First Isomorphism Theorem I can prove that none exit. Prove that Ghas normal subgroups of indexes 2 and 5. By the First Isomorphism Theorem, Z 8 Z 2=ker(˚) ˘=Z 4 Z 4: Thus, jker(˚)j= jZ 8 Z 2j jZ 4 Z 4j = 16 16 = 1: Hence, the kernel is trivial, i. How many homomorphisms are there from Z20 onto Z8 how many are there to Z8? There is no homomorpphism from Z20 onto Z8. The integers Z are a cyclic group. How manyare there to Z10? AI Recommended Answer: There are six homomorphisms from Z20 onto Z10. Find the kernel Kof φ. This suggests that the People's. If φ : Z20 → Z8 is a homomorphism then the order of φ(1) divides gcd(8,20) = 4 so φ(1) is in a unique subgroup of order 4 which is 2Z8. Show your reasoning,. How many homomorphisms are there from ℤ20 onto ℤ10 (surjective/onto homomorphisms)? How many are there to ℤ10 ? (arbitrary homomorphisms) How many are there into ℤ10 ?. How many homomorphisms are there from $\mathbb{Z}_{30}$ onto $\mathbb{Z}_{12}$? 0. The kernel consists of those n n for which qn = 1 q n = 1. Homomorphisms between fields are injective. f ( 0) = f ( 1 ∗ 0) = f ( 1) ∗ f ( 0) = f ( 1) ∗ 0 = 0. As [1] noted, the problem of deciding whether there is a homomorphism from a loop-free. How many are there to Z8? Kernal ( Homomorphisms) Prove that φ : Z ⊕ Z → Z by φ(a, b) = a − b is a homomorphism. Search Join/Login. Q: How many homomorphisms are there from Z20 onto Z10? How manyare there to Z10? How manyare there to Z10? A: To find: Number of homomorphisms from Z20 onto Z10 and the number of homomorphisms to Z10. A map ˚: G! Hbetween two groups is a homor-. 2: Suppose V,W are two vector spaces and T : V −→W is a function (set. This question was created from Chapter 3-Guide to Solve Application. • Chapter 8: #14 Solution: even though D n has a cyclic subgroup (of rotations) of order n, it is not isomorphic to Z n ⊕Z 2 because the latter is Abelian while D n is not. Determine all homomorphisms from S 4 to Z 2. Also, Z = h−1i because k = (−k) · (−1) for each k ∈ Z. Find the order of D4 and list all normal subgroups in D4. Let f : G → H be a homomorphism of groups. (b) Find a homomorphism f : Z20 → Z, such that | ker(f)] = 5. On the other hand, we have 0 = 12 in Z12, and thus φ(0) = φ(12) = φ(1)+···+φ(1) = 12φ(1). Case 2: |im f|=5. It is surjective if it uses every vertex of H. Mathematics 310 Robert Gross Homework 7 Answers 1. How many homomorphisms are there from Z20 onto Z8? There is no homomorpphism from Z20 onto Z8. Question: (2) Find all homomorphisms φ:Z20→Z8. Now, let’s examine homomorphisms to Z10. (a) How many homomorphisms are there from Z24 to Z15? How many are onto? How many are one-to-one?(b)How many isomorphisms (automorphisms) are there from Zn to itself?(c)When will there be an onto homomorphism from Zn to Zm？In the case that there is at least one, how many are there?(d)When will. $\begingroup$ Since $1$ generates $\mathbb Z$, $\Phi(1)$ generates the image of $\mathbb Z$. We say that φ is a ring homomorphism if for every a and b ∈ R, φ(a + b) = φ(a) + φ(b) φ(a · b) = φ(a) · φ(b), and in addition φ(1) = 1. hypnopimp, rough lesbo porn
That is, every element of G has a preimage under the map Φ. . How many homomorphisms are there from z20 onto z10
Since the kernel of ϕ must be a subgroup of $\mathbb{Z}_7$, there are only two possible kernels, $\{0\}$ and all of $\mathbb{Z}_7$. (2) (10. Hence, φ(1) is either 1, 3, 7, or 9. G00 are homomorphisms, then the composite map γφ: G→ G00 is a homomorphism. Answer link. However, I'm confused about how to find out how many of these homomorphisms are onto. Determine all ring homomorphisms from Z Z to Z. In this case, Z6 consists of the elements. There is one relation in $\mathbb Z_{20}$, namely $20=0$. Therefore, by computation, ker ϕ = A 4. So the total number of homomorphisms Dp → Sp is ap + p! where ap is the number of σ ∈ Sp for which σ2 = 1. Let D4 denote the group of symmetries of a square. Determine the kernel of o. On the other hand, we have 0 = 12 in Z12, and thus φ(0) = φ(12) = φ(1)+···+φ(1) = 12φ(1). Log On Test Calculators and Practice Test. Write down the formulas for all homomorphisms from Z into Z10. Thus, in the same way as for group. Question: 25p) 4. f is onto. Macauley (Clemson) Lecture 4. for instance, f (1). Remember also that for a group homomorphism ˚: G!G0it's always true that ˚(e) = e0. na ≡ 0 mod m and a. But I don't know how to proceed and find them all. Exercise 1. Solutions for Chapter 10 Problem 20E: How many homomorphisms are there from Z20 onto Z8? How many are there to Z8?. Since F is an isomorphism by assumption, it is onto and a. Determine all homomorphisms from Zn to itself. I am guessing this is because it is both a group and ring homomorphism?. Step 1 of 5. Definition 2. Since Gis Abelian, (gh) = ghgh= g2h2 8g;h2G, hence is a morphism. If φ : Z20 → Z8 is a homomorphism then the order of φ(1) divides gcd(8,20) = 4 so φ(1) is in a unique subgroup of order 4 which is 2Z8. 117k 7 71 167. How many homomorphisms are there from Z20 onto Z8 Surjective )? How many are there to Z8? There is no homomorpphism from Z20 onto Z8. Thus, the total number is 5. of ring homomorphism from Zn to Zn = No. The attempt at a solution. Question: 20. 2 2: All ring homomorphisms from Z Z to Z ×Z Z × Z. If that is the case for you, then there is at most one ring homomorphism. Thus there are no onto maps. (b) There is a group homomorphism ˚: Z Z Z !Z 7 Z Z sending (n 1;n 2. How many homomorphisms are there from Z 20 onto Z 10? How many are there to Z 10? Expert Solution Want to see the full answer? Check out a sample Q&A here See Solution. Since these group has the same number of elements and φ is onto, φ has to be one-one. The paper should make predictions for Hispanic electoral performance in that state 2020. A homomorphism that is both injective (one-to-one) and surjective (onto) is called an isomorphism of groups. Modified 8 months ago. 20) How many homomorphisms are there from Z 20 onto Z 8? How many are there to Z 8? Proof. How many homomorphisms are there from Z 20 onto Z 10? How many are there to Z 10? 26. Question: 6. This map is onto. Definitely Identity element which is of order 1. A map ˚: G! Hbetween two groups is a homor-. How many homomorphisms are there from $\Bbb Z_{20}$ onto $\Bbb Z_{8}$? How many are there to $\Bbb Z_{8}$? abstract-algebra. Then 2˚(x=2) = ˚(x) = 1, but there is no integer nwith 2n= 1. Find step-by-step solutions and your answer to the following textbook question: $$ \begin{array} { l } { \text { Suppose that the number of homomorphisms from } G \text { to } H \text { is } n. f is an onto mapping. I argue there are exactly two homomorphisms from Z to Z: the trivial map f (a) = 1 and the identity map f (a) = a, and thus that there is only one onto homomorphism from Z to Z. Now, let’s examine homomorphisms to Z10. Section3describes some homomorphisms in lin-ear algebra and modular arithmetic. The kernel of a homomorphism is where e is the identity of H. A: To find: Number of homomorphisms from Z20 onto Z10 and the number of homomorphisms to Z10. So if the homomorphism sends 1 to q q in Q∗ Q ∗, then it sends an arbitrary integer n n to qn q n. Thus possible homomorphisms are of the form x → 2i · x where i = 0,1,2,3. Suppose that G is a finite group with subgroups A and B. But this would mean that 8 divides jgjwhich in turn, by Lagrange, implies that 8 divides 20, which is nonsense. Determine all homomorphisms from Z to S 3. This implies 8 divides 20, which is a contradiction. Given monoids M1 and M2, we say that f : M1 → M2 is a homomorphism if. Thus J 5 is in fact homomorphically equivalent to the core C 5. Indeed, any cyclic group looks like Z/nZ Z / n Z for n ≥ 0 n ≥ 0. Advanced Math questions and answers. If € = 1, then Zzo is the trivial group and there is only one homomorphism from Zzo to any group, which sends every element to the identity element. Exercise 4. So there are at least. which implies that f(3) = 1. How many homomorphisms are there from z20 onto z10 how many are there to z10 6127d6b27dec5304418eb8f3 earth science Questions & Answers Experts answer in as fast as 30 minutes. Then φ(1) must have an order that divides 10 and that divides 20. Let A = a1,a2 and G = A a free group of rank 2. Prove that if ’: G!His a group homomorphism and Gis cyclic, then the subgroup ’(G) is cyclic. Question: a) Describe all the homomorphisms from Z20 to Z40. Note that the question is asked in exercises for rings yet the question just mentions homomorphisms and doesn't specify group or ring. There is only one normal subgroup of order 2 in D4 namely {I,r^2} where R is my rotation. Question: (1) For each of the following homomorphisms verify for yourself that they are homomorphisms and then find the given kernels, images, and or pre-images. I know how to find kernel in others notations, but this one makes me very confused. There is no set of all homomorphisms, so there’s no way to define the size. If ker(f) = S4 there is only 1 homomorphism. Pure maths with Usama. Sorted by: 4. Which of these are valid? Note that we must have ϕ ( x) 20 = 1 and ϕ ( x) 8 = 1. Homomorphisms A group is a set with an operation which obeys certain rules. Conversely, from $\Bbb Z_n$ to $\Bbb Z$ I get that there exists only one homomorphism namely the 0 homomorphism. Is Z4 Z15 isomorphic to Z6 Z10? Therefore Z4 × Z10 ∼ = Z2 × Z20. See Answer. This is the only example, in this list, with non-commutative groups, other than the symmetric group Sn (13. But r5 = 1 r 5 = 1, so the image of r r is the one in V4 V 4, the only element of order dividing 5 5 in V4 V 4. By property (2). Sorted by: 4. 4 How many homomorphisms h satisfy h(012. There are no homomorphisms from Z20 onto Z8 because if there were such a homomorphism, say `, then by the flrst isomorphism theorem Z20=Ker` »= Z8. However, I'm confused about how to find out how many of these homomorphisms are onto. (2) (10. 2 b. How many homomorphisms are there from Z 20 onto Z 8? How many are there to Z 8?. determine all homomorphisms from Z10 to Z20. How many homomorphisms are there from Z 20 onto Z 8 How many are there to Z 8? There is no homomorpphism from Z20 onto Z8. . maya bihou