# Radical subgroup for a fusion system

From Groupprops

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

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## Definition

Suppose is a group of prime power order and is a fusion system on . A subgroup of is termed a -radical subgroup if . Here, denotes the automorphisms of in the category , denotes the p-core, and denotes the inner automorphism group of , viewed as a subgroup of .