Bireflectionality in special orthogonal groups

2024/09/30 by Nielsen, Klaus · 1 citation
#15A15 #15F10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2409.20088

Abstract

It is shown that a transformation in the special orthogonal group SO(V) of a nondefective quadratic space over a field K is bireflectional (product of 2 involutions) if and only if it is reversible (conjugate to its inverse). Furthermore, all elements of SO(V) are bireflectional if and only if dim V is odd or divisible by 4, or V is a hyperbolic plane over GF(2) or GF(3).

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• Products of strictly hyperbolic conjugacy classes in symplectic groups

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