Inductive McKay condition for finite simple groups of type C

2016/12/12 by Marc Cabanes, Cabanes, Marc, Britta Späth +1 · 3 citations
Mathematics · #20C33 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Primary 20C15 #Representation Theory (math.RT) #Secondary 20G40

paper · pdf · doi:10.48550/arxiv.1612.03741

openalex publication_date 2016/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We verify the inductive McKay condition for simple groups of Lie type C, namely finite projective symplectic groups. This contributes to the program of a complete proof of the McKay conjecture for all finite groups via the reduction theorem of Isaacs-Malle-Navarro and the classification of finite simple groups. In an important step we use a new counting argument to determine the stabilizers of irreducible characters of a finite symplectic group in its outer automorphism group. This is completed by analogous results on characters of normalizers of Sylow d-tori in those groups.

Cited by

• The Picky Conjecture for groups of Lie type
• The Isaacs--Navarro Galois conjecture
• Generic weights for finite reductive groups

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