Proof that $H \cap K$ is a group if $H$ and $K$ are subgroups of $G$
39469
If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
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?
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
150042
Prove $x^{-1}Hx$ is a subgroup of $G$
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
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 $G$
98542
Prove that $H$ is a subgroup of an abelian group $G$
65037
$H$ is a maximal normal subgroup of $G$ if and only if $G/H$ is simple.
58033
$G\times H\cong G$ with $H$ non-trivial
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
100974
Showing H is a normal subgroup by calculating left and right coset
28108
Proving the kernel is a normal subgroup.
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
156941
Subgroups of $\mathbb{Z}$
24181
Showing that $G$ is a group under an alternative operation.