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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On finite groups admitting a special noncoprime action


Author: Gülin Ercan
Journal: Proc. Amer. Math. Soc. 133 (2005), 2543-2547
MSC (2000): Primary 20D10, 20F28
Published electronically: April 8, 2005
MathSciNet review: 2146197
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Abstract | References | Similar Articles | Additional Information

Abstract: An important result of Turull (1984) is the following:

Let $GA$ be a finite solvable group, $G \lhd GA$ and $(\vert G\vert, \vert A\vert) = 1$. Then $f (G) \leq f (C_G (A)) + 2 \ell (A)$, where $f$denotes the Fitting height and $\ell$ denotes the composition length.

The purpose of this work is to give a treatment of the minimal configuration in this framework with additional conditions, yet without the coprimeness condition.


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Additional Information

Gülin Ercan
Affiliation: Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08011-1
PII: S 0002-9939(05)08011-1
Keywords: Noncoprime action, fitting height
Received by editor(s): May 17, 2004
Published electronically: April 8, 2005
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.