Order of a factor group and whether it is cyclic
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
107716
Show that $G$ is cyclic
125960
Factor groups of matrices
126098
Isomorphism of factor groups
102634
Order of the Rubik's cube group
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
152071
Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$
151025
If G is a group of order n=35, then it is cyclic
14528
Proof that all abelian simple groups are cyclic groups of prime order
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
106653
How many generator has a cyclic group of order n?
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
53357
Cyclic Group Generators of Order $n$
62035
Order of automorphism group of cyclic group
5089
An element of a group has the same order as its inverse
17178
Order of $\phi(g)$ divides the order of $g$