Exotic fusion systems

Duration: 45 mins 29 secs

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Description:	Graziar, V Tuesday 25th February 2020 - 11:00 to 12:00


Created:	2020-02-28 12:39
Collection:	Groups, representations and applications: new perspectives
Publisher:	Isaac Newton Institute
Copyright:	Graziar, V
Language:	eng (English)


Abstract:	Fusion systems are structures that encode the properties of conjugation between p-subgroups of a group, for p any prime number. Given a finite group G, it is always possible to define the saturated fusion system realized by G on one of its Sylow p-subgroups S: this is the category where the objects are the subgroups of S and the morphisms are the restrictions of conjugation maps induced by the elements of G. However, not all saturated fusion systems can be realized in this way. When this is the case, we say that the fusion system is exotic. The understanding of the behavior of exotic fusion systems (in particular at odd primes) is still an important open problem. In this talk we will offer a new approach to the study of exotic fusion systems at odd primes. We will show that an important role is played by the fusion systems defined on p-groups of maximal nilpotency class and we will present new results concerning the classification of such fusion systems.

Abstract:

Fusion systems are structures that encode the properties of conjugation between p-subgroups of a group, for p any prime number. Given a finite group G, it is always possible to define the saturated fusion system realized by G on one of its Sylow p-subgroups S: this is the category where the objects are the subgroups of S and the morphisms are the restrictions of conjugation maps induced by the elements of G. However, not all saturated fusion systems can be realized in this way. When this is the case, we say that the fusion system is exotic. The understanding of the behavior of exotic fusion systems (in particular at odd primes) is still an important open problem. In this talk we will offer a new approach to the study of exotic fusion systems at odd primes. We will show that an important role is played by the fusion systems defined on p-groups of maximal nilpotency class and we will present new results concerning the classification of such fusion systems.

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