Computing the projective indecomposable modules of large finite groups.

Let G be a finite group and F be a finite field. A projective indecomposable F G-module is an indecomposable direct summand of the group algebra F G. Computing the projective indecomposable modules of large finite groups has been always a challenging problem due to the large sizes of the representations of these groups. This dissertation describes a new algorithm for constructing the projective indecomposable modules of large finite groups. This algorithm uses the condensation techniques as described in [12]. The power of the algorithm will be illustrated by the examples of the socle series of all projective indecomposable modules of the sporadic simple Mathieu group M24 and the simple alternating group A12 in characteristic 2.