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New posts in normal-subgroups
If $HK$ is a subgroup of $G$ (where $H$ and $K$ are subgroups of $G$), then are $H$ and $K$ normal in $HK$?
abstract-algebra
group-theory
normal-subgroups
How to show that the commutator subgroup is a normal subgroup
abstract-algebra
group-theory
normal-subgroups
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
abstract-algebra
group-theory
normal-subgroups
Why do we define quotient groups for normal subgroups only?
group-theory
normal-subgroups
quotient-group
Normal subgroup of prime index
abstract-algebra
group-theory
finite-groups
normal-subgroups
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