On the vertices of indecomposable summands of certain Lefschetz modules

Details On the vertices of indecomposable summands of certain Lefschetz modules On the vertices of indecomposable summands of certain Lefschetz modules

2011-09-27

arxiv.org/abs/1109.5761v1

Mathematics

Group Theory

30 pages

Scientific paper

We study the reduced Lefschetz module of the complex of p-radical and p-centric subgroups. We assume that the underlying group G has parabolic characteristic p and the centralizer of a certain noncentral p-element has a component with central quotient H a finite group of Lie type in characteristic p. A non-projective indecomposable summand of the associated Lefschetz module lies in a non-principal block of G and it is a Green correspondent of an inflated, extended Steinberg module for a Lie subgroup of H. The vertex of this summand is the defect group of the block in which it lies.

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