Hostname: page-component-76c49bb84f-7l7zb Total loading time: 0 Render date: 2025-07-08T09:36:31.254Z Has data issue: false hasContentIssue false
  • English
  • Français

Nilpotent injectors and conjugacy classes in solvable groups

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Geoffrey R. Robinson
Geoffrey R. Robinson
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B 15 2 TT, England
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.

We provide an upper bound for the order of a nilpotent injector of a finite solvable group with Fitting subgroup of order n. We also show that the same bound is an upper bound for the number of conjugacy classes, provided that the k(G V)-conjecture holds for solvable G all primes dividing n.

MSC classification

Secondary: 20E45: Conjugacy classes 20F16: Solvable groups, supersolvable groups

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 3 , December 2001 , pp. 349 - 352
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Gluck, D. and Magaard, K., ‘The extra-special case of the k(G V)-problem’, preprint, 1999.Google Scholar
[2]Isaacs, I. M., Character theory of finite groups, Pure Appl. Math. 69 (Academic Press, New York, 1976).Google Scholar
[3]Köhler, C. and Pahlings, H., ‘Regular orbits and the k(G V)-problem, in: Groups and computation III. (Columbus, OH, 1999) Ohio State Univ. Math. Res. Inst. Publ. 8 (deGruyter, Berlin, 2001), pp. 209–228.CrossRefGoogle Scholar
[4]Kóvacs, L. G. and Robinson, G. R., ‘On the number of conjugacy classes of finite groups’, J. Algebra 160 (1993), 441–460.Google Scholar
[5]Thompson, J. G., private communication, (circa 1989).Google Scholar
[6]Winter, D. L., ‘p-solvable linear groups of finite order’, Trans. Amer Math. Soc. 157 (1971), 155–160.Google Scholar