Graded Lie rings with many commuting components and an application to 2-Frobenius groups

Khukhro, E. I. (2008) Graded Lie rings with many commuting components and an application to 2-Frobenius groups. Bulletin of the London Mathematical Society, 40 (5). pp. 907-912. ISSN 0024-6093

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Item Type:Article
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Abstract

The following variations of the theorems of Higman, Kreknin, and Kostrikin are proved: let L be a (/n)-graded Lie ring with trivial zero-component L0 = 0; if for some m each grading component commutes with all but at most m components, then L is soluble of derived length bounded above in terms of m; if, in addition, n is a prime, then L is nilpotent of class bounded above in terms of m. As an application to 2-Frobenius groups, it is proved that if a finite Frobenius group BC with complement C of order t acts on a finite group A so that AB is also a Frobenius group, (t, A) = 1, and CA(C) is abelian, then A is nilpotent of class bounded above in terms of t. © 2008 London Mathematical Society.

Keywords:Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15592
Deposited On:04 Jan 2016 17:10

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