Subgroup fully normalized by a category

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This article defines a property that can be evaluated for a group of prime power order, equipped with a fusion system
View other such properties

Definition

Suppose P is a group of prime power order and \mathcal{F} is a category on P. A subgroup R of P is termed fully normalized by \mathcal{F} if, for any Q \le P such that Q and R are isomorphic via \mathcal{F}, |N_P(Q)| \le |N_P(R)|.

The definition is typically used when \mathcal{F} is a fusion system on P.