Computing the projective indecomposable modules of large finite groups
AdvisorLux, Klaus M.
Committee ChairLux, Klaus M.
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PublisherThe University of Arizona.
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AbstractLet G be a finite group and F be a finite field. A projective indecomposable FG- module is an indecomposable direct summand of the group algebra FG. 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 . 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.