If every Left Cosets of H are Right Cosets of H, show that H is normal in G
109517
A subgroup such that every left coset is contained in a right coset.
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
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 $G$
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
116786
normal subgroups of Alternating group
28108
Proving the kernel is a normal subgroup.
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
44165
the image of normal subgroups
23533
All subgroups normal $\implies$ abelian group
124179
Proof that every metric space is normal
154398
Show that H is a subgroup of G
64582
Group covered by finitely many cosets
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
71819
Prove that $H$ is normal.
83273
Show that $o(gHg^{-1})=o(H)$