Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T15:04:35.018Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain relations between p-regular class sizes and the p-structure of p-solvable groups

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Antonio Beltrán  and
María José Felipe
Antonio Beltrán
Affiliation:
Department o de Matemáticas, Universidad Jaume I, Castellón 12071, Spain e-mail: [email protected]
María José Felipe
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Valencia 46022, Spain e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a finite p-solvable group for a fixed prime p. We study how certain arithmetical conditions on the set of p-regular conjugacy class sizes of G influence the p-structure of G. In particular, the structure of the p-complements of G is described when this set is {1, m, n} for arbitrary coprime integers m, n > 1. The structure of G is determined when the noncentral p-regular class lengths are consecutive numbers and when all of them are prime powers.

MSC classification

Secondary: 20E45: Conjugacy classes 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 387 - 400
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Beltrán, A. and Felipe, M. J., ‘On the diameter of a p-regular conjugacy class graph of finite groups’, Comm. Algebra 30 (2002), 5861–5873.CrossRefGoogle Scholar
[2]Beltrán, A. and Felipe, M. J., ‘Finite groups with two p-regular conjugacy class lengths’, Bull. Austral. Math. Soc. 67 (2003), 163–169.CrossRefGoogle Scholar
[3]Bertram, E. A., Herzog, M. and Mann, A., ‘On a graph related to conjugacy classes of groups’, Bull. London Math. Soc. 22 (1990), 569–575.CrossRefGoogle Scholar
[4]Bianchi, M., Chillag, C., Mauri, A. G. B., Herzog, M. and Scoppola, C. M., ‘Applications of a graph related to conjugacy classes in finite groups’, Arch. Math. 58 (1992), 126–132.CrossRefGoogle Scholar
[5]Bianchi, M., Gillio, A. and Casolo, C., ‘A note on conjugacy class sizes of finite groups’, Rend. Sem. Mat. Univ. Padova 106 (2001), 255–260.Google Scholar
[6]Chillag, D. and Herzog, M., ‘On the lengths of the conjugacy classes of finite groups’, J. Algebra 131 (1990), 110–125.CrossRefGoogle Scholar
[7]Dolfi, S. and Lucido, M. S., ‘Finite groups in which p′-classes have q′-length’, Israel J. Math. 122 (2001), 93–115.CrossRefGoogle Scholar
[8]Lu, Z. and Zhang, J., ‘On the diameter of a graph related to p-regular conjugacy classes of finite groups’, J. Algebra 231 (2000), 705–712.CrossRefGoogle Scholar