Abstract Algebra group question

Question

If $G$ be a finite group of $l$ elements. Suppose that $a$ belongs to $G$, and $\mathrm{ord}(a)=k$,can $k>l$?

I think $k$ can't be bigger than $l$, because $k$ should equal $l$.

Correct. The order of an element has to divide the order of the group. — Ian Coley, Oct 29 '13 at 07:39

score 1 · Answer 1 · answered Oct 29 '13 at 07:41

1

Hint: Show that the cyclic subgroup $\langle a \rangle$ has cardinality $k$.

answered Oct 29 '13 at 07:41

Seirios

1 Answers1