Is it true that $gHg^{-1}\subset H\implies gHg^{-1}= H$?
41085
Conjugate subgroup strictly contained in the initial subgroup?
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
83273
Show that $o(gHg^{-1})=o(H)$
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
62566
Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?
154001
$(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
79367
Understanding the difference between two theorems related to $|G\,:\,K|=|H\,:\,K|\cdot|G\,:\,H|$.
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
111515
Proving that $-a=(-1)\cdot a$
55976
Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?