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 |