Publikationsdetails

Generalized bases of finite groups

verfasst von
Benjamin Sambale
Abstract

Motivated by recent results on the minimal base of a permutation group, we introduce a new local invariant attached to arbitrary finite groups. More precisely, a subset Δ of a finite group G is called a p-base (where p is a prime) if ⟨ Δ ⟩ is a p-group and C G(Δ) is p-nilpotent. Building on results of Halasi–Maróti, we prove that p-solvable groups possess p-bases of size 3 for every prime p. For other prominent groups, we exhibit p-bases of size 2. In fact, we conjecture the existence of p-bases of size 2 for every finite group. Finally, the notion of p-bases is generalized to blocks and fusion systems.

Organisationseinheit(en)
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Typ
Artikel
Journal
Archiv der Mathematik
Band
117
Seiten
9-18
Anzahl der Seiten
10
ISSN
0003-889X
Publikationsdatum
07.2021
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Mathematik (insg.)
Elektronische Version(en)
https://doi.org/10.1007/s00013-021-01589-x (Zugang: Offen)