On finite groups admitting a special noncoprime action

Ercan, Gülin

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

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
DOI: https://doi.org/10.1090/S0002-9939-05-08011-1
Published electronically: April 8, 2005
MathSciNet review: 2146197
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Abstract: An important result of Turull (1984) is the following:

Let 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 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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