let φ: G-H be an isomorphism of groups show that Z(G)≌Z(H)
158975
Isomorphism of centers of isomorphic groups
126098
Isomorphism of factor groups
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 $D_p$
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
15000
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
152603
Group isomorphic to its automorphism group
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
67199
Isomorphism $H_n(D^n, S^{n - 1};A)$ and $A$
54911
The preimage of a normal subgroup under a group homomorphism is normal
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
58707
Prove Quotient Group Isomorphism
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
61732
Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$
37928
Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$