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