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2012-04

On the dimensions of PIM's

by Conchita Martínez-Pérez, Wolfgang Willems.


Series: 2012-04, Preprints

MSC:
20C20 Modular representations and characters
20C05 Group rings of finite groups and their modules
20C30 Representations of finite symmetric groups
20C33 Representations of finite groups of Lie type

Abstract:
We discuss the structure of finite groups for which the projective indecomposable modules have special given dimensions.
In particular, we prove the converse of Fong's dimension formula for p-solvable groups. Furthermore,
we characterize groups for which all irreducible p-Brauer characters have p-power degrees.

Keywords:
character degrees, indecomposable modules, p-solvable groups