Q-1: Let ( G,*) be a goup. Prove that if x-1 = x V x e G, then G is abelian. Is the connerse to this stafenert claim - true ? Prove your

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.7: Direct Sums (optional)
Problem 14E: 14. Let be an abelian group of order where and are relatively prime. If and , prove that .
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Q.1: tet (G,+)
be a
group.
Prove that if
x-1 = x
V x e G,
then
G is abelian.
Is the connerse to this stafenent
claim -
true ? Prove your
Transcribed Image Text:Q.1: tet (G,+) be a group. Prove that if x-1 = x V x e G, then G is abelian. Is the connerse to this stafenent claim - true ? Prove your
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