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Publicly Available Published by De Gruyter March 26, 2014

On the Fitting height of factorised soluble groups

  • Carlo Casolo EMAIL logo , Enrico Jabara and Pablo Spiga
From the journal Journal of Group Theory

Abstract

In this paper we are concerned with finite soluble groups G admitting a factorisation G=AB, with A and B proper subgroups having coprime order. We are interested in bounding the Fitting height of G in terms of some group-invariants of A and B, including the Fitting heights and the derived lengths.

We express our gratitude to Evgeny Khukhro for bringing to our attention the main result of [Infinite Groups and Related Algebraic Structures, Akademiya Nauk Ukrainy, Kiev (1993), 393–404], which resulted in a nice improvement on an earlier version of Theorem 1.1.

Received: 2013-11-18
Revised: 2014-2-21
Published Online: 2014-3-26
Published in Print: 2014-9-1

© 2014 by De Gruyter

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