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On the definability of radicals in supersimple groups
Published online by Cambridge University Press: 12 March 2014
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.
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- Copyright © Association for Symbolic Logic 2013
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