A finiteness condition on centralizers in locally nilpotent groups

We give a detailed description of infinite locally nilpotent groups G such that the index | C G ( x ) : ⟨ x ⟩ | is finite, for every ⟨ x ⟩ ⋪ G . We are also able to extend our analysis to all non-periodic groups satisfying a variation of our condition, where the requirement of finiteness is replaced...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Monatshefte für Mathematik 2017-02, Vol.182 (2), p.289-298
Hauptverfasser:	Fernández-Alcober, Gustavo A., Legarreta, Leire, Tortora, Antonio, Tota, Maria
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Oil field equipment
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We give a detailed description of infinite locally nilpotent groups G such that the index \| C G ( x ) : ⟨ x ⟩ \| is finite, for every ⟨ x ⟩ ⋪ G . We are also able to extend our analysis to all non-periodic groups satisfying a variation of our condition, where the requirement of finiteness is replaced with a bound.
ISSN:	0026-9255 1436-5081
DOI:	10.1007/s00605-015-0854-0