Normaliser

In group theory, the normaliser of a subgroup of a group (mathematics) is the set of all group elements which map the given subgroup to itself by conjugation.

Formally, for H a subgroup of a group G, we define


 * $$ N_G(H) = \{ g \in G : g^{-1}Hg = H \} . \, $$

A subgroup of G is normal in G if its normaliser is the whole of G.

The normaliser of the trivial subgroup is the whole group G.