On families of nilpotent subgroups and associated coset posets

Gritschacher, Simon und Villarreal, Bernardo (2022): On families of nilpotent subgroups and associated coset posets. In: Journal of Homotopy and Related Structures, Bd. 17, Nr. 4: S. 493-509

Abstract

We study some properties of the coset poset associated with the family of subgroups of class <= 2 of a nilpotent group of class <= 3. We prove that under certain assumptions on the group the coset poset is simply-connected if and only if the group is 2-Engel, and 2-connected if and only if the group is nilpotent of class 2 or less. We determine the homotopy type of the coset poset for the group of 4 x 4 upper unitriangular matrices over F-p, and for the Burnside groups of exponent 3.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 2193-8407
• Sprache: Englisch