Normaliser

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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.

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