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On the dimensions of PIM's

by Conchita Martínez-Pérez, Wolfgang Willems.

Series: 2012-04, Preprints

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

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.

character degrees, indecomposable modules, p-solvable groups