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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 15, Issue 6


On the vertices of indecomposable summands of certain Lefschetz modules

John Maginnis / Silvia Onofrei
  • Department of Mathematics, The Ohio State University, 100 Mathematics Tower, 231 West 18 Avenue, Columbus, Ohio 43210, USA
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Published Online: 2012-11-01 | DOI: https://doi.org/10.1515/jgt-2012-0028


We study the reduced Lefschetz module of the complex of p-centric and p-radical subgroups. We assume that the underlying group G has parabolic characteristic p and the centralizer of a certain noncentral p-element has a component with central quotient H a finite group of Lie type in characteristic p. A nonprojective indecomposable summand of the associated Lefschetz module lies in a nonprincipal block of and it is a Green correspondent of an inflated, extended Steinberg module for a Lie subgroup of H. The vertex of this summand is the defect group of the block in which it lies. The application of these results to sporadic finite simple groups yields nine groups when and eight groups when for which the reduced Lefschetz module has precisely one nonprojective summand.

About the article

Received: 2011-11-04

Revised: 2012-07-26

Published Online: 2012-11-01

Published in Print: 2012-11-01

Citation Information: Journal of Group Theory, Volume 15, Issue 6, Pages 737–773, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2012-0028.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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