Products of nonprimary cyclic conjugacy classes in the general linear group

Abstract

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 $m,k\ne 0$. It is shown that the product of two nonsingular (m,k)-cyclic conjugacy classes $\Omega$ and $\Psi$ of GL(m+k,K) contains all nonscalar matrices P in GL(m+k,K) with determinant $\det P=\det \Omega \Psi$.

minor corrections and improvements