Answered: subgroups of G. Let x,y e G. We define…

subgroups of G. Let x,y e G. We define the relation x ~ y by the following definition: x ~ y iff y = axb for some a e A, b e B. Prove that this relation is an equivalence rel

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 30E

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Question

Let G be a group and let A and B be subgroups of G. Let x,y e G. We define the relation x ~ y by the following definition: x ~ y iff y = axb for some a e A, b e B. Prove that this relation is an equivalence relation on G.

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