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ON THE $p$-LENGTH AND THE WIELANDT LENGTH OF A FINITE $p$-SOLUBLE GROUP

Part of: Representation theory of groups

Published online by Cambridge University Press:  07 March 2013

NING SU  and
YANMING WANG
NING SU
Affiliation:
School of Mathematics, Sun Yatsen University, Guangzhou, 510275, PR China email mc04sn@mail2.sysu.edu.cn
YANMING WANG*
Affiliation:
Lingnan College and School of Mathematics, Sun Yatsen University, Guangzhou, 510275, PR China
*
✉stswym@mail.sysu.edu.cn
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Abstract

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The $p$-length of a finite $p$-soluble group is an important invariant parameter. The well-known Hall–Higman $p$-length theorem states that the $p$-length of a $p$-soluble group is bounded above by the nilpotent class of its Sylow $p$-subgroups. In this paper, we improve this result by giving a better estimation on the $p$-length of a $p$-soluble group in terms of other invariant parameters of its Sylow $p$-subgroups.

Keywords

p-lengthWielandt lengthnilpotent classpermutable

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 453 - 459
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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