<1: 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: 4. x~y iff y = axb for some a e A, be B Prove that this relation is an equivalence relation on G.
<1: 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: 4. x~y iff y = axb for some a e A, be B Prove that this relation is an equivalence relation on G.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:<1:
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:
4.
x~y iff y = axb for some a e A, be B
Prove that this relation is an equivalence relation on G.
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