Determination of Socle Series using the Condensation Method

摘要

We show how the condensation method introduced by R.A.Parker can be applied to determine the socle series of a finite-dimensional representation of a group over a finite field. We develop several new techniques for this approach and illustrate their power by the example of the socle series of all projective indecomposable representations of the sporadic simple Mathieu group M_23 in characteristic 2.