A local approach to stability groups

In this short note we prove a local version of Philip Hall’s theorem on the nilpotency of the stability group of a chain of subgroups by only using elementary commutator calculus (Hall’s theorem is a direct consequence of our result). This provides a new way of dealing with stability groups.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of algebraic combinatorics 2024-09, Vol.60 (2), p.599-602
Hauptverfasser:	Newell, Martin L., Trombetti, Marco
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Commutators Computer Science Convex and Discrete Geometry Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Stability Subgroups Theorems
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	In this short note we prove a local version of Philip Hall’s theorem on the nilpotency of the stability group of a chain of subgroups by only using elementary commutator calculus (Hall’s theorem is a direct consequence of our result). This provides a new way of dealing with stability groups.
ISSN:	0925-9899 1572-9192
DOI:	10.1007/s10801-024-01345-8