On finite groups admitting a special noncoprime action
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- Proc. Amer. Math. Soc. 133 (2005), 2543-2547 Request permission
Abstract:
An important result of Turull (1984) is the following: Let $GA$ be a finite solvable group, $G \lhd GA$ and $(|G|, |A|) = 1$. 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.References
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Additional Information
- Güli̇n Ercan
- Affiliation: Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey
- Received by editor(s): May 17, 2004
- Published electronically: April 8, 2005
- Communicated by: Jonathan I. Hall
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 2543-2547
- MSC (2000): Primary 20D10, 20F28
- DOI: https://doi.org/10.1090/S0002-9939-05-08011-1
- MathSciNet review: 2146197