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)