H,K be two abelian subgroups of G.Will HK be a subgroup of G?
124709
Suppose G be a non-abelian group and H,K be two abelian subgroups of G. Then must HK be an abelian subgroup of G?
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other
61379
Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.
71035
Non abelian subgroup of a abelian group.
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
39469
If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
43750
Subgroups of finite solvable groups. Solvable?
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
102979
If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
64408
Subgroup of $\mathbb{Q}$ with finite index
71232
if $A$ is Abelian group , $B$ is subgroup of $A$ , Is $B \times A/B \cong A$?
57809
For which $n$, $G$ is abelian?
157145
Subgroup of $S_8$ isomorphic to $G$
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 $G=HK$?
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian