On finite groups admitting a special noncoprime action

Ercan, Güli̇n

doi:10.1090/S0002-9939-05-08011-1

On finite groups admitting a special noncoprime action
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by Güli̇n Ercan

Proc. Amer. Math. Soc. 133 (2005), 2543-2547

DOI: https://doi.org/10.1090/S0002-9939-05-08011-1

Published electronically: April 8, 2005

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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.

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