Prove that if G is a cyclic group with more than 2 elements, then there always exists an isomorphism ϕ:G→G that is not the identity mapping
133348
Is isomorphism not always unique?
104460
When a group is cyclic
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
27728
Question on a homomorphism of a set G.
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
151047
a non trivial example: $G/H$ is isomorphic to $G$
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
28210
A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
18540
Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
92430
Show that the group is cyclic.
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
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 $G$?