Fusion invariant characters of p-groups

verfasst von

Benjamin Sambale

Abstract

We consider complex characters of a p-group P, which are invariant under a fusion system (Formula presented.) on P. Extending a theorem of Bárcenas–Cantarero to non-saturated fusion systems, we show that the number of indecomposable (Formula presented.) -invariant characters of P is greater or equal than the number of (Formula presented.) -conjugacy classes of P. We further prove that these two quantities coincide whenever (Formula presented.) is realized by a p-solvable group. On the other hand, we observe that this is false for constrained fusion systems in general. Finally, we construct a saturated fusion system with an indecomposable (Formula presented.) -invariant character, which is not a summand of the regular character of P. This disproves a recent conjecture of Cantarero–Combariza.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Communications in algebra

ISSN

0092-7872

Publikationsdatum

24.12.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.1080/00927872.2024.2439491 (Zugang: Offen)