Nilpotent groups of semilinear transformations which are monomial

Nilpotent groups of semilinear transformations which are monomial

Let <em>H</em> be a nilpotent subgroup of<em> ΓL_n (q) = <φ> GL_n (q)</em>, where <em>φ</em> denotes the field automorfism induced by the Frobenius map. We give a condition on the primes dividing<em> |H ∩ GL_n (q)|</em> under which <em>H<...

Full description

Bibliographic Details
Main Authors:	Andrea Lucchini, M. Chiara Tamburini
Format:	Article
Language:	English
Published:	Università degli Studi di Catania 2008-11-01
Series:	Le Matematiche
Subjects:	Nilpotent groups Carter subgroups
Online Access:	http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/58

Description
Summary:	Let <em>H</em> be a nilpotent subgroup of<em> ΓL_n (q) = <φ> GL_n (q)</em>, where <em>φ</em> denotes the field automorfism induced by the Frobenius map. We give a condition on the primes dividing<em> \|H ∩ GL_n (q)\|</em> under which <em>H</em> is conjugate to a subgroup of the generalized monomial group<em> <φ> Diag_n (F∗_q ) Sym(n)</em>.<br />We show an application of this result to the determination of Carter subgroups of finite groups.<br /><p> </p>
ISSN:	0373-3505 2037-5298