Computing Projective Indecomposable Modules and Higher Cohomology Groups

Abstract

We describe the theory and implementation in Magma of algorithms to compute the projective indecomposable KG-modules for finite groups G and finite fields K. We describe also how they may be used together with dimension-shifting techniques to compute cohomology groups Hⁿ (G, M) for finite-dimensional KG-modules M and n⩾3.

2000 AMS Subject Classification:

• Primary 20C40
• Secondary 20C2S
• 20J06

Keywords:

• groups
• computing
• projective modules
• cohomology

ACKNOWLEDGMENTS

We are grateful to Klaus Lux and Jürgen Müller for helpful conversations and comments on the text.