Character tables and defect groups

verfasst von

Benjamin Sambale

Abstract

Let B be a block of a finite group G with defect group D. We prove that the exponent of the center of D is determined by the character table of G. In particular, we show that D is cyclic if and only if B contains a “large” family of irreducible p-conjugate characters. More generally, for abelian D we obtain an explicit formula for the exponent of D in terms of character values. In small cases even the isomorphism type of D is determined in this situation. Moreover, it can read off from the character table whether |D/D^′|=4 where D^′ denotes the commutator subgroup of D. We also propose a new characterization of nilpotent blocks in terms of the character table.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Journal of algebra

Band

562

Seiten

323-340

Anzahl der Seiten

18

ISSN

0021-8693

Publikationsdatum

15.11.2020

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2007.04919 (Zugang: Offen)
https://doi.org/10.1016/j.jalgebra.2020.05.040 (Zugang: Geschlossen)