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A generalization of a theorem of Camina and Herzog

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An old result of Camina and Herzog states that a finite group G has abelian Sylow 2-subgroups, provided |G : CG(x)| is odd for any 2-element xG. In my talk, I will report about a generalization of this theorem to saturated fusion systems, which was conjectured by Kühlshammer, Navarro, Sambale and Tiep. This does not only lead to a significant simplification of the proof of the theorem of Camina and Herzog, but also implies a new result in block theory. In my talk I will explain the proof of the main result and give an introduction to the theory of fusion systems along the way.

The talk will be accessible to PhD students.

This talk is part of the Algebra seminar series.

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