Finite group of even order has an element $g \neq e$ such that $g^ 2 = e$
26398
Group of even order contains an element of order 2
47478
Show that any cyclic group of even order has exactly one element of order $2$
5089
An element of a group has the same order as its inverse
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
30676
$G'$ and the product of all the elements in an odd order group
58397
Every cyclic group with order > 2 has at least 2 distinct generators
128692
Example of an infinite group where every element except identity has order 2
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
152741
Cardinal of a group $G$ such that for all $x\in G$ we have $x^2=e$
143550
Order of product of two elements in an abelian group
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
19458
Finite groups and Normal subgroups - $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$.
36882
Two finite abelian groups with the same number of elements of any order are isomorphic
122125
Order of group element divides order of finite group
28210
A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
56607
gcd and order of elements of group