If $K<H\triangleleft G$, does it follow that $K\triangleleft G$?
13523
Are normal subgroups transitive?
102979
If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
80996
A canonical construction proving $\left|HK\right| = \left|H\right|\left|K\right| / \left|H \cap K\right|$?
111024
Does $gHg^{-1}\subseteq H$ imply $gHg^{-1}= H$?
95976
Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG?
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
157840
Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?