Almost group theory

Abstract : The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having infinite index in its predecessor stabilizes after finitely many steps. The Fitting subgroup of such groups is shown to be nilpotent and a theorem of Hall for nilpotent groups is generalized to ind-definable almost nilpotent subgroups of $\widetilde{\mathfrak M}\_c$-groups.
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Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01206954
Contributeur : Nadja Hempel <>
Soumis le : mercredi 16 novembre 2016 - 20:47:13
Dernière modification le : jeudi 15 mars 2018 - 10:31:31
Document(s) archivé(s) le : jeudi 16 mars 2017 - 15:50:56

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Nadja Hempel. Almost group theory. 2015. 〈hal-01206954v3〉

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