Subgroup of finite abelian group $G$ isomorphic to $G/H$
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
47623
The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
134858
Abelian Group Homomorphism
59211
Product of Finite Abelian Group
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
23279
Group Theory Isomorphism
46116
Proof of the First Isomorphism Theorem for Groups
133770
Subgroups of finite abelian groups.
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
119512
If H ≤ Z(G) ≤ G, where G is a finite group,Z(G) is its center, and (G:H) = p for some prime p, then G is abelian.
126098
Isomorphism of factor groups