• Sep 14th 2009, 12:18 PM
krohrs311
Let G be a group with a finite number of elements. Show that for any a in G, there exists an n in the positive integers such that a^n = e.

The hint is to consider e, a, a^2, a^3, ...., a^m, and use the cancellation laws. Thanks :)
• Sep 14th 2009, 12:39 PM
Swlabr
Quote:

Originally Posted by krohrs311
Let G be a group with a finite number of elements. Show that for any a in G, there exists an n in the positive integers such that a^n = e.

The hint is to consider e, a, a^2, a^3, ...., a^m, and use the cancellation laws. Thanks :)

HINT: $a^{m_1}=a^{m_2}$ for some $m_1 \neq m_2 \in \mathbb{N}$, because we are in a finite group.