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On the definability of radicals in supersimple groups

Published online by Cambridge University Press:  12 March 2014

Cédric Milliet
Cédric Milliet*
Affiliation:
Université Galatasaray, Faculté de Sciences et de Lettres, Département de Mathématiques, Çirağan Caddesi N. 36, 34357 Ortaköy, Istamboul, Turquie, E-mail:milliet@math.univ-lyon1.fr
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Abstract

If G is a group with a supersimple theory having a finite SU-rank, then the subgroup of G generated by all of its normal nilpotent subgroups is definable and nilpotent. This answers a question asked by Elwes, Jaligot, Macpherson and Ryten. If H is any group with a supersimple theory, then the subgroup of H generated by all of its normal soluble subgroups is definable and soluble.

Keywords

Supersimple groupFitting subgroupsoluble radical
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 649 - 656
Copyright
Copyright © Association for Symbolic Logic 2013

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