A reduction theorem for the Character Triple Conjecture

2024/02/16 by Damiano Rossi, Rossi, Damiano · 1 citation
Engineering · Mathematics · #20C20 (20C15) #Advanced Combinatorial Mathematics #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2402.10632

openalex publication_date 2024/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the Character Triple Conjecture holds for all finite groups once assumed for all quasi-simple groups. This answers the question on the existence of a self-reducing form of Dade's conjecture, a problem that was long investigated by Dade in the 1990s. Our result shows that this role is played by the Character Triple Conjecture, recently introduced by Späth, that we present here in a general form free of all previously imposed restrictions.

Cited by

• A reduction theorem for the blockwise Navarro Alperin weight conjecture via H-triples

Related

• Character Triple Conjecture for p-Solvable Groups
• A reduction theorem for the Galois-McKay conjecture
• The Character Triple Conjecture for maximal defect characters and the prime 2
• On a conjecture of Navarro and Tiep on character fields
• Character triples and relative defect zero characters