How to show that a the group $( \mathbb{Z} / n \mathbb{Z} )^* $ has elements of order $2$
82571
Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
18881
Number of elements of order $7$ in a group
2731
Groups of even order have an element whose order is 2.
53409
Show group of order $4n + 2$ has a subgroup of index 2.
81354
The product of all the elements of a finite abelian group
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
30676
$G'$ and the product of all the elements in an odd order group
61732
Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
102971
Product of all elements of a finite group with an unique element of order 2
26398
Group of even order contains an element of order 2
125640
Group of order $p^2$ is abelian.
96123
Element of maximal order in alternating group $A_{10}$: how to prove this is it?
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
48393
Abelian groups of order n.