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Bounding the Diameter of the Brauer Graph of a Block of a Solvable Group

Part of: Representation theory of groups

Published online by Cambridge University Press:  17 December 2015

James P. Cossey  and
Mark L. Lewis
James P. Cossey
Affiliation:
Department of Theoretical and Applied Mathematics, University of Akron, Akron, OH 44325, USA (cossey@uakron.edu)
Mark L. Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA (lewis@math.kent.edu)
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Abstract

We define several graphs related to the p-blocks of a solvable group. We bound the diameter of these graphs when the defect group associated with the block is either abelian or normal and when the group has odd order. We give examples to show that these bounds are met.

Keywords

graphsdiameterBrauer characterssolvable 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 59 , Issue 3 , August 2016 , pp. 591 - 603
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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