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Preprint Number 444

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444. Cédric Milliet
On the definability of radicals in supersimple groups

Submission date: 24 April 2012.


If G is a group with supersimple theory having finite SU-rank, 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 a group with supersimple theory, the subgroup of H generated by all of its normal soluble subgroups is definable and soluble.

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