Groups of p-central type

verfasst von

Benjamin Sambale

Abstract

A finite group G with center Z is of central type if there exists a fully ramified character λ∈ Irr (Z) , i. e. the induced character λ^G is a multiple of an irreducible character. Howlett–Isaacs have shown that G is solvable in this situation. A corresponding theorem for p-Brauer characters was proved by Navarro–Späth–Tiep under the assumption that p≠ 5 . We show that there are no exceptions for p= 5 , i. e. every group of p-central type is solvable. Gagola proved that every solvable group can be embedded in G/Z for some group G of central type. We generalize this to groups of p-central type. As an application we construct some interesting non-nilpotent blocks with a unique Brauer character. This is related to a question by Kessar and Linckelmann.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Mathematische Zeitschrift

Band

306

Anzahl der Seiten

9

ISSN

0025-5874

Publikationsdatum

24.11.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://doi.org/10.1007/s00209-023-03406-3 (Zugang: Offen)