Order of an element in a cyclic group
13807
Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
92430
Show that the group is cyclic.
122125
Order of group element divides order of finite group
122959
How is number of conjugacy class related to the order of a group?
33300
Showing order of $Z (G) =1$ or $pq$
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
81116
$gh = hg, \ \gcd(|g|, |h|) = 1\Rightarrow|gh| = |g||h|\ \ (|a|$ = order of element $a)$
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
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 $G$
28676
Is a finite group uniquely determined by the orders of its elements?
131946
Order of an Element Under a Homomorphism
84789
Order of products of elements in a finite Abelian group
1577
Order of nontrivial elements is 2 implies Abelian group
28913
How to find a generator of a cyclic group?
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
106653
How many generator has a cyclic group of order n?
98734
Order of a product of elements in a generic group