# Group of prime power order with no exotic fusion system

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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

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A **group of prime power order with no exotic fusion system** is a group of prime power order that does not admit any exotic fusion system. In other words, every saturated fusion system on it arises as the fusion system induced by a finite group containing it as a Sylow subgroup.

## 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 | Resistant group of prime power order|FULL LIST, MORE INFO | |||

resistant group of prime power order | identity functor controls strong fusion |