"p-Local block theory of

p-solvable groups"





(Bilkent University)


Abstract: For a prime p, a p-block of a finite group G is a primitive idempotent b of the centre of the group algebra FG, where F is an algebraically closed field of characteristic p. The fusion system
of G and the fusion system of b, actually the origins of the notion of a fusion system, are easier to define than fusion systems in abstract, in fact, they can be defined from scratch quite quickly.
Now supposing that G is p-solvable, the p-block theory can be done by working inductively using the Fong Correspondence which, by deep results
of Puig, preserves fusion systems. In the situation where the Fong Correspondence does not yield a strict reduction, one can apply a theorem of Hall and Higman to show that the fusion system of b coincides with the fusion system of G. All of this is old theory, done by Puig long before others appreciated the concepts, but it is not easily extractable from the literature. Some chunks of this introductory seminar will be accessible to those with only some knowledge of ordinary character theory.
If time permits, we shall comment on adaptation of the methods to our study of multiplicity modules and Kuelshammer--Puig classes in thep-solvable case.


Date:  Tuesday, 9 February 2016

Time: 13:40 - 15:30 

Place: Mathematics Seminar Room, SA-141


All are most cordially invited. Tea and biscuits after the seminar.