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List Question

Proving that if $H$ is not normal, then $HgH$ is not a left coset for some $g \in G$.

Isomorphism between isomorphic abelian groups quotiented by isomorphic subgroups

The intersection of normal subgroups

$G$ finite metabelian group, $P$ a Sylow $p$-subgroup. Show that $P'$ is abelian and normal in $G$

Transitive Group and its Normal Subgroup

True or false: $H \cap K= 1$, $H$ centralizes $K \implies K=1$?

$H=A^B^$ abelian: $A^$ centralizes $S$, $B^$ centralizes $T\implies H$ centralizes $S \cap T$

If $p> \sqrt{|G|}$ divides $|G|$, then $G$ contains a normal subgroup of order $p$

Meaning of factorization of groups

Quotient groups from the orbit category

Quotient group in solvable connected Lie group is isomorphic to real numbers or torus

Let $H,K \leq G$ s.t $H,K$ two different Sylow $p$-subgroups of $G$. Prove $HK$ isn't a subgroup of $G$.

If $G$ has a normal series then a subgroup $H$ of $G$ also have one

The only proper normal subgroups of a nonabelian quasisimple group are subgroups of its centre.

Finite group generated by two finite subgroups

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