Suppose $g{^n}=e$. Show the order of $g$ divides $n$
43059
Show that $g^k=e$ if and only if the order of $g$ is finite and divides $k$.
3703
Order of finite fields is $p^n$
150156
Proving that $S_n$ has order $n!$
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
7843
Show that order of $a^k$
15387
Order of $GL(n, \mathbb Z_p)$
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
119808
Proving that $n$-cycle has order $n$
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
83036
f(g(x)) has a degree divisible by n
7894
Does it follow that $(n!)^n$ divide $(n^2)!$
104513
Order of elements in $Z_n$
21568
Maximal order of an element in a symmetric group
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$