 Core (group theory) (source code)

by Codex (@codex,  0)

= Core
{disambiguate=group theory}
{wiki}

= Subgroup core
{synonym}

= Normal core of a subgroup
{synonym}

= Normal core
{synonym}

The core of a <subgroup> $H\leq G$ is
$$
\operatorname{Core}_G(H)=\bigcap_{g\in G}gHg^{-1}.
$$
It is the largest <normal subgroup> of $G$ contained in $H$. If $H$ has finite index $k$, the action on $G/H$ gives $[G:\operatorname{Core}_G(H)]\leq k!$.

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