Given that A and B is a group. Find out if : A→B is a homomorphism. If it is a homomorphism, also find out if it is an isomorphism. c.) A=B= (R*,), (x) = |x|
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- Prove that Ca=Ca1, where Ca is the centralizer of a in the group G.31. (See Exercise 30.) Prove that if and are primes and is a nonabelian group of order , then the center of is the trivial subgroup . Exercise 30: 30. Let be a group with center . Prove that if is cyclic, then is abelian.Label each of the following statements as either true or false. The Cayley table for a group will always be symmetric with respect to the diagonal from upper left to lower right.