Computing the projective indecomposable modules of large finite groups

Persistent Link:
http://hdl.handle.net/10150/193610
Title:
Computing the projective indecomposable modules of large finite groups
Author:
Kalaycioglu, Selin
Issue Date:
2009
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Let 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 [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.
Type:
text; Electronic Dissertation
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Lux, Klaus M.
Committee Chair:
Lux, Klaus M.

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleComputing the projective indecomposable modules of large finite groupsen_US
dc.creatorKalaycioglu, Selinen_US
dc.contributor.authorKalaycioglu, Selinen_US
dc.date.issued2009en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.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 [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.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLux, Klaus M.en_US
dc.contributor.chairLux, Klaus M.en_US
dc.contributor.committeememberUlmer, Douglas L.en_US
dc.contributor.committeememberPickrell, Douglas M.en_US
dc.contributor.committeememberTiep, Pham H.en_US
dc.identifier.proquest10443en_US
dc.identifier.oclc659752075en_US
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