K. Nielsen

collaborators

4 papers

math.GR2026

Conjugacy classes with covering number two in hyperbolic orthogonal groups

Klaus Nielsen

There is a conjecture, usually attributed to J. G. Thompson, that a finite simple nonabelian group $G$ has a conjugacy class $Ψ$ of covering number 2; i.e $G = Ψ^{2}$ . We show that t…

math.GR2026

Products of involutons in symplectic groups II

Klaus Nielsen

We show that the symplectic groups Sp(2n, K) over a field $K$ are 5-reflectional if $2 n \geq 4$ . If $n$ is even and $(2 n, K) \neq = (4, GF (3))$ they are even 4-reflectional.

math.GR2026

Products of nonprimary cyclic conjugacy classes in the general linear group

Klaus Nielsen

A cyclic square matrix (and its conjugacy class) C over a field K is called (m,k)-cyclic if it has a decomposition $C = A \oplus B$ , where $dim A = m, dim B = k$ and $m, k \neq = 0$ …

math.GR2026

On the traces of the product of 2 linear similarity classes

Klaus Nielsen

It is shown that the product of two nonscalar conjugacy classes of the special linear group SL $(n, K)$ contains matrices of arbitrary trace if $n \geq 4$ and $K$ is an abitrary field…