If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator?
53357
Cyclic Group Generators of Order $n$
12667
How many subgroups of order $n$ does $D_n$ have?
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
84501
Proof involving Cyclic group, generator and GCD
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
122959
How is number of conjugacy class related to the order of a group?
139100
A question on the group algebra $k[G]$ of a finite abelian group
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
106653
How many generator has a cyclic group of order n?
147596
Number of solutions to $x^n=e$ in group $G$ is divisible by $n$
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
58397
Every cyclic group with order > 2 has at least 2 distinct generators
96680
Generators of symmetric group $S_n$
88344
Order of a group and subsequent subgroups
151025
If G is a group of order n=35, then it is cyclic
55976
Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?