Products of involutions in symplectic groups I: bireflections

2025/07/15 by Klaus Nielsen, Nielsen, Klaus
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2507.11056

openalex publication_date 2025/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify bireflectional elements (products of 2 involutions) in symplectic groups Sp(2n, K) over a field K. We also classify rev ersible elements (elements conjugate to their inverses) and bireflectional elements in finite projective symplectic groups PSp(2n,q).

Citations

• Products of involutions in symplectic groups over general fields (I)
• Products of two involutions in orthogonal and symplectic groups

Related

• Products of two involutions in orthogonal and symplectic groups
• Products of involutions in symplectic groups over general fields (II)
• Products of involutions in symplectic groups over general fields (I)
• A note on bireflectional elements of an algebra
• Bireflectionality in the commutator subgroup of a finite orthogonal group