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Fusion systems and sporadic J-components

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If you have a question about this talk, please contact David Craven.

Properly interpreted, a J-component in a 2-fusion system F is a component K in the centralizer C of some involution with the property that the 2-rank of C is the 2-rank of F. I will explain how these fit into Michael Aschbacher’s framework for a classification of simple 2-fusion systems of odd type, and then describe a classification of such F when K is the 2-fusion system of one of several sporadic groups, under the assumption that the “centralizer” of K in F is cyclic. Of particular interest is the case in which K is the 2-fusion system of the Hall-Janko group.

This is joint work with Julianne Rainbolt.

This talk is part of the Algebra Seminar series.

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