**BILKENT **

**FUSION SYSTEMS
SEMINAR**

**"Fusion
Systems of Blocks: Part I"**

By

# LAURENCE BARKER

# (Bilkent University)

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**Abstract: **We
understand a block of a ring to be a primitive idempotent of the centre of the ring.
We shall be considering blocks of FG, where F is a large field of prime
characteristic p and G is a finite group. In the 1940s, Brauer
introduced the notion of a defect group D of a block b of FG. Such D is a p-subgroup
of G, well-defined up to conjugacy. He also considered pairs (P, e) where P is
a p-subgroup and e is a block of C(P) with defect
group Z(P). In 1979, Alperin
and Broue defined a Brauer pair
to be a pair (P, e), as above, but without the condition on the defect group of
e. In modern terminology, the pairs originally considered by Brauer are the centric Brauer
pairs. The fusion system of b is a
category whose objects are the Brauer pairs
containing (1, b). Usually, we pass to an equivalent subcategory whose objects
can be identified with the subgroups of a defect group D. Puig
observed that the centric condition on a Brauer pair
can be described entirely in terms of the fusion system.

**Date: ****Tuesday, October 20, 2015**

**Time: ****15.40**

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

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**All are most cordially invited.**

Tea and biscuits: before the seminar