**Department of Mathematics**

**BÝLKENT
ALGEBRAIC **

TOPOLOGY SEMINAR

**" Reduced Fusion Systems Over Small 2-Groups"**

By

# BOB OLIVER

**(Université
PARIS 13)**

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**Abstract:
**The sectional rank of a
finite p-group is the largest rank of any abelian subquotient. The sectional p-rank of a finite group is the
sectional rank of
its Sylow p-subgroups. I will describe a result
listing all reduced, indecomposable fusion systems over 2-groups of sectional rank at most
four. This is motivated by a theorem of Gorenstein
and Harada, where they listed all finite simple groups of sectional 2-rank at
most four. The new result contains no surprises: the fusion systems in
question are all those of simple groups on the Gorenstein-Harada
list. But the method of proof seems very different, since it is based on
studying the different types of essential subgroups which can occur, rather
than the centralizers of involutions. This also leads to a different way
of organizing the final result, which I hope will be of interest.

**Date: ****Monday, April 21, 2014**

**Time: ****13.40-15.00**

**Place: ****Mathematics Seminar Room,
SA-141**

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**All are most cordially invited.**

Tea and cookies will be served after the talk.