Group of even order contains an element of order $2$ (Explanation)
26398
Group of even order contains an element of order 2
69833
Number of elements not equal to their inverses is even number
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
51196
A group of order $p^2q^2$ is never simple
124224
How many groups of order $n$ with center {e} exist?
63499
Groups of prime squared order
134376
Let $G$ be a nonabelian group. Let $a \in G$ have order $4$ and let $b \in G$ have order $3$. Then the order of the element $ab$ in $G$
128692
Example of an infinite group where every element except identity has order 2
142038
Finding the number of elements of order two in the symmetric group $S_4$
140673
how to find the order of an element in a quotient group
119758
On the order of elements of $\mathrm{GL}(2,q)$.
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
126893
A group of order 2p (p prime) and other conditions - prove abelian.
102634
Order of the Rubik's cube group
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
121423
Prove that every element of a finite group has an order
61550
Existence of elements of order $p^k$ in a finite group