Automizers as extended reflection groups

Details Automizers as extended reflection groups Automizers as extended reflection groups

2010-10-21

arxiv.org/abs/1010.4340v1

Mathematics

Group Theory

Scientific paper

Brou\'e, Malle and Michel have shown that the automizer of an abelian Sylow p-subgroup in a finite simple Chevalley group is an irreducible complex reflection group, for p not too small and different from the defining characteristic. The aim is this note is to show that a suitable version of this property holds for general finite groups. As an example, the automizer of an 11-Sylow subgroup in the Monster is the 2-dimensional complex reflection group G_{16}.

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