There exist elements of finite order $n$ in $GL_2(\Bbb Z)$ for every positive $n$.
46687
Elements of $GL_{2}(\mathbb{Z})$ of finite order
129750
Order of $SL_2(\mathbb{Z}/ n\mathbb{Z})$
53357
Cyclic Group Generators of Order $n$
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
104855
Prove that $N \subset Z(G)$
104513
Order of elements in $Z_n$
59535
Prove that there exists such a set of $n$ positive integers
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
93474
A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$
35660
Elements of order 2 in $D_{2n}$
1577
Order of nontrivial elements is 2 implies Abelian group
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
26398
Group of even order contains an element of order 2
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
47478
Show that any cyclic group of even order has exactly one element of order $2$
156319
Show that a group with $|G| = 33$ contains an element of order $3$