2024/05/04 by Clément de Seguins Pazzis, Pazzis, Clément de Seguins
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2405.02663
openalex publication_date 2024/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let s be an n-dimensional symplectic form over a field \mathbbF of characteristic other than 2, with n>2. In a previous article, we have proved that if \mathbbF is infinite then every element of the symplectic group Sp(s) is the product of four involutions if n is a multiple of 4 and of five involutions otherwise. Here, we adapt this result to all finite fields with characteristic not 2, with the sole exception of the very special situation where n=4 and |\mathbbF|=3, a special case which we study extensively.