Resumen de Torsion matrices over communicative integral group rings

Sudarshan K. Sehgal, Gregory T. Lee

• Let ${\mathbb Z}A$ be the integral group ring of a finite abelian group $A$, and $n$ a positive integer greater than 5. We provide conditions on $n$ and $A$ under which every torsion matrix $U$, with identity augmentation, in $GL_n({\mathbb Z}A)$ is conjugate in $GL_n({\mathbb Q}A)$ to a diagonal matrix with group elements on the diagonal. When $A$ is infinite, we show that under similar conditions, $U$ has a group trace and is stably conjugate to such a diagonal matrix.