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June 2013 On the definability of radicals in supersimple groups
Cé{d}ric Milliet
J. Symbolic Logic 78(2): 649-656 (June 2013). DOI: 10.2178/jsl.7802160

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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Cé{d}ric Milliet. "On the definability of radicals in supersimple groups." J. Symbolic Logic 78 (2) 649 - 656, June 2013. https://doi.org/10.2178/jsl.7802160

Information

Published: June 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1314.03036
MathSciNet: MR3145200
Digital Object Identifier: 10.2178/jsl.7802160

Subjects:
Primary: 03C45, 03C60
Secondary: 20F16, 20F18

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 2 • June 2013
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