Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T06:24:10.411Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Mark L. Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA ([email protected])
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Cossey, J. P. and Lewis, M. L., Lifts of partial characters with cyclic defect groups, J. Austral. Math. Soc. 89 (2010), 145–163.CrossRefGoogle Scholar
2. Dolfi, S., Large orbits in coprime actions of solvable groups, Trans. Am. Math. Soc. 360 (2008), 135–152.Google Scholar
3. Feit, W., The representation theory of finite groups (North Holland, Amsterdam, 1982).Google Scholar
4. Fong, P. and Srinivasan, B., Brauer trees in classical groups, J. Alg. 131 (1990), 179–225.Google Scholar
5. Harris, M. and Linckelmann, M., Splendid derived equivalences for blocks of finite p-solvable groups, J. Lond. Math. Soc. (2) 62 (2000), 85–96.Google Scholar
6. Isaacs, I. M., Characters of π-separable groups, J. Alg. 86 (1984), 98–128.CrossRefGoogle Scholar
7. Isaacs, I. M., Fong characters in π-separable groups, J. Alg. 99 (1986), 89–107.Google Scholar
8. Isaacs, I. M., Partial characters of π-separable groups, Prog. Math. 95 (1991), 273–287.Google Scholar
9. Isaacs, I. M., Characters of finite groups (American Mathematical Society, Providence, RI, 2006).Google Scholar
10. Manz, O. and Wolf, T. R., Representations of solvable groups (Cambridge University Press, 1993).CrossRefGoogle Scholar
11. Moretó, A. and Wolf, T. R., Orbit sizes, character degrees, and Sylow subgroups, Adv. Math. 184 (2004), 18–36.CrossRefGoogle Scholar
12. Navarro, G., Characters and blocks of finite groups (Cambridge University Press, 1998).Google Scholar
13. Thevenaz, J., G-algebras and modular representation theory (Oxford University Press, 1995).Google Scholar