If G is a finite Abelian group, and H is a subgroup of G, How can I prove that G/H is isomorphic to another subgroup N of G?.
51352
Subgroups of a finite abelian group
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
57809
For which $n$, $G$ is abelian?
59811
Finite Abelian groups with the same number of elements for all orders are isomorphic
18415
Direct sum of Abelian groups and Isomorphism
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
137949
If the quotient group $G/N$ be isomorphic to $G_2$, is $G$ isomorphic to $G_1\times G_2$ where $N$ is isomorphic to $G_1$?
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
23279
Group Theory Isomorphism
87766
Using Cayley's Theorem to find an isomorphic subgroup.