Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-10T12:47:38.953Z Has data issue: false hasContentIssue false
  • English
  • Français

The number of blocks with a given defect group

Part of: Representation theory of groups

Published online by Cambridge University Press:  26 February 2010

Laurence Barker
Laurence Barker
Affiliation:
Department of Mathematics, Bilkent University., 06533 Bilkent, Ankara, Turkey.
Get access

Extract

Given a p-subgroup P of a finite group G we express the number of p-blocks of G with defect group P as the p-rank of a symmetric integer matrix indexed by the N(P)/P-conjugacy classes in PC(P)/P. We obtain a combinatorial criterion for P to be a defect group in G.

MSC classification

Secondary: 20C20: Modular representations and characters

Information

Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997 , pp. 368 - 373
Copyright
Copyright © University College London 1997

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.)

Article purchase

Temporarily unavailable

References

1.Alperin, J. L.. Weights for finite groups. Proc. Symp. Pure Math., 47 (1987), 369–379.CrossRefGoogle Scholar
2.Broué, M.. On a theorem of G. Robinson. J. London Math. Soc., 29 (1984), 425–434.CrossRefGoogle Scholar
3.Broué, M. and Robinson, G. R.. Bilinear forms on G-algebras. J. Algebra. 104 (1986), 377–396.Google Scholar
4.Iizuka, K. and Watanabe, A.On the number of blocks of irreducible characters of a finite group with a given defect group. Kumamoto J. Sci. (Math.), 9 1973, 55–61.Google Scholar
5.Robinson, G. R.. The number of blocks with a given defect group, J. Algebra, 84 (1983), 493– 502.Google Scholar
6.Strunkov, S. P.. Strunkov. Existence and the number of p-blocks of defect 0 in finite groups. Algebra and Logic, 30 (1992), 231–241.Google Scholar