(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let G be a group with a finite number of elements. Show that for any a in G, there exists an n in Z+ such that a^{n}=e.

2. Relevant equations

a hint is given: consider e, a, a^{2},...a^{m}, where m is the number of elements in G, and use the cancellation laws.

3. The attempt at a solution

so part of the trouble i'm having (i'm guessing the most important part), is figuring out what they're asking. is the number n i'm looking for a number that when any a in G is raised to, it gives the identity? i.e. (i'm just picking random letters) a^{n}= e and b^{n}=e when a and b are not equal but n is the same in both? i was working on this question for a while thinking it to mean that a particular a^{p}might have n_{0}while a^{q}might have n_{1}to take it to e (identity).

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# Homework Help: Help clarifying a question regarding (i think) cyclic groups

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