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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]
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Abstract

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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

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