Cyclic group $G$ with generator $ab$.
56607
gcd and order of elements of group
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?
92430
Show that the group is cyclic.
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
103216
The set $\{g^2 | g \in G\}$ in a group $G$
39895
Showing a free abelian group is generated by its basis
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
38687
Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
24181
Showing that $G$ is a group under an alternative operation.
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.