Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question
Describe Aut(Zp), the automorphism group of the cyclic group Zp where p is prime. In particular find the order of this group. (Hint: A generator must map to another generator)
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- Consider the set of permutations V = {(1), (1 2) (3 4), (1 3) (2 4), (1 4) (2 3)}. Determine whether V forms a group under the operation of composition. If it is a group, is the group cyclic? If it is a group, is the group abelian?arrow_forwardsuppose H is cyclic group. The order of H is prime. Prove that the group of automorphism of H is cyclic. And also find its order.arrow_forwardAbstract Algebraarrow_forward
- is it a binary option? is it associative? identity element= inverse elements=arrow_forwardLet G = Zp × Zp. Is this group cyclic? As you know any cyclic group canbe generated by one element. If G is not cyclic how many elements you need to generate this group. What is the smallest size of a generating set?arrow_forward
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