Year: 2024
Type: article
Abstract: We consider complex characters of a p-group P, which are invariant under a fusion system F on P. Extending a theorem of Bárcenas-Cantarero to nonsaturated fusion systems, we show that the number of indecomposable Finvariant characters of P is greater or equal than the number of F -conjugacy classes of P. We further prove that these two quantities coincide whenever F 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 F -invariant character, which is not a summand of the regular character of P.This disproves a recent conjecture of Cantarero-Combariza.
Source: Communications in Algebra
Author: Benjamin Sambale
Institution: Leibniz University Hannover
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405739841