Chapter 5, problem 8b Consider a cyclic group G and two positive integers A and B with the following two properties: (1). group G's order is A; (2) A divides B. Prove the number of elements in group G with order B is ϕ(B).

Chapter 5, problem 8b Consider a cyclic group G and two positive integers A and B with the following two properties: (1). group G's order is A; (2) A divides B. Prove the number of elements in group G with order B is ϕ(B).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...

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Question

Chapter 5, problem 8b

Consider a cyclic group G and two positive integers A and B with the following two properties: (1). group G's order is A; (2) A divides B.

Prove the number of elements in group G with order B is ϕ(B).

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