- #1

RJLiberator

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## Homework Statement

If G is a group with n elements and g ∈ G, show that g^n = e, where e is the identity element.

## Homework Equations

## The Attempt at a Solution

I feel like there is missing information, but that cannot be.

This seems too simple:

The order of G is the smallest possible integer n such that g^n = e. If no such n exists, then G is of infinite order.

From this definition of order can we simply state that since G is a group with 'n' elements then there must exist an n such that g^n = e ?

order is denoted as °(g)

So

°(g) = n ==> g^n = e.