The Loewy structure of the projective indecomposable modules for A_{10} in characteristic 3

TL;DR

This paper determines the Loewy structure of projective indecomposable modules for the alternating group A_{10} over a field of characteristic 3, providing detailed algebraic insights into their composition series.

Contribution

It offers the first explicit computation of the Loewy structure for these modules, advancing understanding of modular representation theory of A_{10}.

Findings

Explicit Loewy structures for all indecomposable projective modules of A_{10} in characteristic 3.

Enhanced understanding of the module category of A_{10} in characteristic 3.

Foundation for further research on modular representations of symmetric and alternating groups.

Abstract

We compute the Loewy structure of the indecomposable projective modules for the group algebra FG, where G is the alternating group on 10 letters and F is an algebraically closed field of characteristic 3.