K. Nielsen

activity

20242026

collaborators

5 papers

math.GR2026

Products of strictly hyperbolic conjugacy classes in symplectic groups

Klaus Nielsen

We call a conjugacy class of the symplectic group Sp $(2 n, K)$ over a field $K$ strictly hyperbolic if its minimal polynomial is of the form $q (x) q^{*} (x)$ , where the polynomial $q(x…

math.GR2025

Products of involutions in symplectic groups I: bireflections

Klaus Nielsen

We classify bireflectional elements (products of 2 involutions) in symplectic groups Sp $(2 n, K)$ over a field $K$ . We also classify rev ersible elements (elements conjugate to thei…

math.GR2024

Bireflectionality in the commutator subgroup of a finite orthogonal group

Klaus Nielsen

We classify the bireflections (products of 2 involutions) in the commutator subgroup G an orthogonal group O(V) over a finite field GF(q) of characteristic not 2. We show that ever…

math.GR2024

Bireflections of the commutator subgroup of an orthogonal group over the reals

Klaus Nielsen

Let $O (p, q)$ be the orthogonal groups of signature $(p, q)$ over the reals. It is shown that an element of the commutator subgroup $O (p, q)^{'}$ of $O (p, q)$ is bireflectional (product o…

math.GR2024

Bireflectionality in special orthogonal groups

Klaus Nielsen

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…