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Lifts and vertex pairs in solvable groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  04 January 2012

James P. Cossey  and
Mark L. Lewis
James P. Cossey
Affiliation:
Department of Theoretical and Applied Mathematics, University of Akron, Akron, OH 44325, USA ([email protected])
Mark L. Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA ([email protected])
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Abstract

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Suppose G is a p-solvable group, where p is odd. We explore the connection between lifts of Brauer characters of G and certain local objects in G, called vertex pairs. We show that if χ is a lift, then the vertex pairs of χ form a single conjugacy class. We use this to prove a sufficient condition for a given pair to be a vertex pair of a lift and to study the behaviour of lifts with respect to normal subgroups.

Keywords

liftsBrauer charactersfinite groupsrepresentationssolvable groups

MSC classification

Secondary: 20C20: Modular representations and characters 20C15: Ordinary representations and characters
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 143 - 153
Copyright
Copyright © Edinburgh Mathematical Society 2011

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