Let G = {1, 3, 5, 9, 11, 13} and let represent the binary operation of multiplication modulo 14. (a) Prove that (G, ) is a group. (You may assume that multiplication is associative.) (b) List the cycl...

Question

Question

Let G = {1, 3, 5, 9, 11, 13} and let represent the binary operation of multiplication modulo 14.

(a) Prove that (G, ) is a group. (You may assume that multiplication is associative.)

(b) List the cyclic subgroups of (G, ).

(c) Explain why (G, ) is not isomorphic to the symmetric group S3.

(d) State an isomorphism between (G, ) and (Z6, +).

Answer 1

Answer #1

1, 3, 5, 9, l, 13f 13 513 3113 5 5 919 13 3 11 1 5 ow Caley Jase we have -j = 11, 11-9, 13-13 b(313,3 , 9,1,n,,j Gis a nc-e db

Answer 2

Similar Homework Help Questions

1. Let G = {a, b, c, d, e} be a set with an associative binary...

1. Let G = {a, b, c, d, e} be a set with an associative binary operation multiplication such that ab = ba = d, ed = de = c. Prove that G under this multiplication cannot consist of a group. Hint: Assume that G under this operation does consist of a group. Try to complete the multiplication table and deduce a contradiction. 2. Let G be a group containing 4 elements a, b, c, and d. Under the group...
Let G be a group of order 231 = 3 · 7 · 11. Let H,...

Let G be a group of order 231 = 3 · 7 · 11. Let H, K and N denote sylow 3,7 and 11-subgroups of G, respectively. a) Prove that K, N are both proper subsets of G. b) Prove that G = HKN. c) Prove that N ≤ Z(G). (you may find below problem useful). a): <|/ is a normal subgroup, i.e. K,N are normal subgroups of G (below problem): Let G be a group, with H ≤ G...
1. Consider the group U(35) = {1, 2, 3, 4, 6, 8, 9, 11, 12, 13,...

1. Consider the group U(35) = {1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 26, 27, 29, 31, 32, 33, 34} under the operation of multiplication modulo 35. The orders of the elements are: g 1112 341689|11|12|13|16|17|18|19|22|23|24|26|27|29|31 | 32 | 33 34 ord(g) | 1 | 12 | 12 62 463 12 4 3 12 12 6 4 12 6 6 4 2 6 12 12 2 a. Find two p-groups...

May 21, 2019 R 3+3+5-11 points) (a) Let X1,X2, . . Xn be a random sample from G distribution. Show that T(Xi, . . . , x,)-IT-i xi is a sufficient statistic for a (Justify your work). (b) Is Unifo...

May 21, 2019 R 3+3+5-11 points) (a) Let X1,X2, . . Xn be a random sample from G distribution. Show that T(Xi, . . . , x,)-IT-i xi is a sufficient statistic for a (Justify your work). (b) Is Uniform(0,0) a complete family? Explain why or why not (Justify your work) (c) Let X1, X2, . .., Xn denote a random sample of size n >1 from Exponential(A). Prove that (n - 1)/1X, is the MVUE of A. (Show steps.)....