Group of order 6 contains an element of of order 3
15210
Group of order 6 proof
68201
Cyclic group of order $n$
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
18881
Number of elements of order $7$ in a group
84132
Number of preimages of a group element under a homomorphism.
123710
Find eight elements in $S_6$ that commute with $(12)(34)(56)$
157806
Order of a element on a Symmetric Group
148904
Groups of order $p^3$
8742
Examples and further results about the order of the product of two elements in a group
7973
Groups of order $pq$ have a proper normal subgroup
93703
Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$
41731
Question about the order of the product of two elements in an abelian group
156319
Show that a group with $|G| = 33$ contains an element of order $3$
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
115746
Find the order of a subgroup of $S_5$ generated by two elements
124428
Elements of the dicyclic group of order 12
93760
There is an element of order $51$ in the multiplicative group $(Z/103Z)^∗.$