In any finite group $G$, the number of elements not equal to their own inverse is an even number.
69833
Number of elements not equal to their inverses is even number
61550
Existence of elements of order $p^k$ in a finite group
40513
A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
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$
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
40846
When can a (finite) group be written as the quotient of some other group by its center?
138862
Product of all elements in an odd finite abelian group is 1
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 $G$
145127
For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
145406
Prove every element of $G$ has finite order.
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
18881
Number of elements of order $7$ in a group
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
35401
Examples of finite groups that are not a semidirect product