# Math Help - groups

1. ## groups

if G is a finite group, does it mean that there wil always be an element g in G where g^k= e, and k is the order if G? or it might not always be the case?

2. Originally Posted by alexandrabel90
if G is a finite group, does it mean that there wil always be an element g in G where g^k= e, and k is the order if G? or it might not always be the case?

If a group $G$ is finite of order $k$ then $g^k=e$ for all elements $g\in G$...this follows at once from Lagrange's theorem.

3. Originally Posted by tonio
If a group $G$ is finite of order $k$ then $g^k=e$ for all elements $g\in G$...this follows at once from Lagrange's theorem.
I think (or hope) that he meant does it follow there is an element of $G$ whose order is the same as the group. The answer is clearly no by considering any non-cyclic group.