Fusion invariant characters of p-groups

authored by

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Communications in algebra

ISSN

0092-7872

Publication date

24.12.2024

Publication status

E-pub ahead of print

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.1080/00927872.2024.2439491 (Access: Open)