If $a^{24}=e$ in a group $G$, what are the possible orders of $a$?
17316
If $a^\phi = 1$ then the order of $a$ divides $\phi$
114187
In a finite cyclic group, the generator has the order of the group
158799
Order of $G$ is 35, are there elements of order 5 and 7 in G?
26449
$|G|=24$ prove that $G$ is not simple
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
79995
G is group of order pq, pq are primes
101596
Determine group G as cyclic
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
84789
Order of products of elements in a finite Abelian group
112165
Classification of groups of order 12
122959
How is number of conjugacy class related to the order of a group?
26398
Group of even order contains an element of order 2
76943
Existence of subgroup of order six in $A_4$
32620
Is every group of order $21$ cyclic?
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 $G$
141458
How many subgroups or order 8 an abelian Group of order 72 can have