Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T11:17:21.523Z Has data issue: false hasContentIssue false
  • English
  • Français

A BOUND ON THE p-LENGTH OF P-SOLVABLE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  26 August 2014

JON GONZÁLEZ-SÁNCHEZ  and
FRANCESCA SPAGNUOLO
JON GONZÁLEZ-SÁNCHEZ
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Spain email: [email protected]
FRANCESCA SPAGNUOLO
Affiliation:
Departament dÀlgebra, Universitat de València; Dr. Moliner, 50, 46100, Burjassot, València, Spain. email: [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 and P a Sylow p-subgroup of G. Suppose that $\gamma_{\ell (p-1)}(P)\subseteq \gamma_r(P)^{p^s}$ for ℓ(p−1) < r + s(p − 1), then the p-length is bounded by a function depending on ℓ.

MSC classification

Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 1 , January 2015 , pp. 167 - 171
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

REFERENCES

1.Fernandez-Alcober, G. A., Gonzalez-Sanchez, J. and Jaikin-Zapirain, A., Omega subgroups of pro-p groups, Isr. J. Math. 166 (2008), 393–412.Google Scholar
2.Gonzalez-Sanchez, J. and Weigel, T. S., Finite p-central groups of height k, Isr. J. Math. 181 (2011), 125–143.Google Scholar
3.Gorenstein, D. E., Finite groups (Chelsea, New York NY, 1980).Google Scholar
4.Hall, P. and Higman, G., The p-length of a p-solvable group and reduction theorems for Burnside's problem, Proc. London Math. Soc. 6 (3) (1956), 1–42.CrossRefGoogle Scholar
5.Khukhro, E. I., On p-solvable groups with a generalized p-central or powerful Sylow p-subgroup, Int. J. Group Theory 1 (2) (2012, June), 51–57 (7).Google Scholar