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