For $1 \leq m \leq n$ there is an element of order $q^m-1$ in $GL_n(\mathbb F_q).$
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
21568
Maximal order of an element in a symmetric group
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
105666
What's an easy way to show that $GL(n,\mathbb C)$ is connected?
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
149056
Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.
15526
Question on groups of order $pq$
65096
$\chi(G)+\chi(G')\leq n+1$
108550
Elements of $\mathbb Q(2^{1/3})$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1