Let G be a finite group, prove that for every a in G there exists a positive integer n such that ...

Question

Question

let G be a finite group, prove that for every a in G there exists a positive integer n such that aⁿ=e, the identity.

Answer 1

Answer #1

Let G be a finite group and a EG Then a -a aEG Then a-aaEG a.a2.aeG Thus for a e G aas,a*--a*-.. are elem ents of G Ifa # e

Answer 2

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