Publikation: On supersimple groups
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2013
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Journal of Algebra. 2013, 373, pp. 426-438. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2012.09.033
Zusammenfassung
An infinite group having a supersimple theory has a finite series of definable subgroups whose factors are infinite and either virtually-FC or virtually-simple modulo a finite FC-centre. We deduce that a group which is type-definable in a supersimple theory has a finite series of relatively definable subgroups whose factors are either abelian or simple groups. In this decomposition, the non-abelian simple factors are unique up to isomorphism.
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Fachgebiet (DDC)
510 Mathematik
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Model theory, supersimple group, just-infinite groups, series with Abelian or simple factors
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MILLIET, Cedric, 2013. On supersimple groups. In: Journal of Algebra. 2013, 373, pp. 426-438. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2012.09.033BibTex
@article{Milliet2013super-26613,
year={2013},
doi={10.1016/j.jalgebra.2012.09.033},
title={On supersimple groups},
volume={373},
issn={0021-8693},
journal={Journal of Algebra},
pages={426--438},
author={Milliet, Cedric}
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<dcterms:abstract xml:lang="eng">An infinite group having a supersimple theory has a finite series of definable subgroups whose factors are infinite and either virtually-FC or virtually-simple modulo a finite FC-centre. We deduce that a group which is type-definable in a supersimple theory has a finite series of relatively definable subgroups whose factors are either abelian or simple groups. In this decomposition, the non-abelian simple factors are unique up to isomorphism.</dcterms:abstract>
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