Resistant group of prime power order

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group of prime power order is termed resistant if, for every saturated fusion system on the group, the identity functor is a conjugacy functor that controls strong fusion in the group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian group of prime power order abelian group of prime power order implies resistant

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
group of prime power order with no exotic fusion system