Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
120971
(Revised) Prove that $\phi$ is a group homomorphism and find the kernel.
63769
Group theory proof of Euler's theorem ($a^{\phi(m)} \equiv 1\mbox{ }(\mbox{mod }m)$ if $\gcd(a,m)=1$)
33455
Question on group homomorphisms involving the standard Z-basis
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
144258
How to show a group is cyclic?
135710
Cyclic Automorphism group
34902
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
151025
If G is a group of order n=35, then it is cyclic
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
98542
Prove that $H$ is a subgroup of an abelian group $G$