Torsion Units in Infinite Group Rings Original Research Article

A conjecture of Zassenhaus says that if G is a finite group then any unit u = ∑ u(g) g of finite order in imageG is conjugate in imageG to ± g, for some g set membership, variant G. This is known to be equivalent to saying that image(g0) = ∑h not, vert, similar g0, u(h) is nonzero for a unique conjugacy class imageg0 of elements of G. We prove that this latter condition holds for infinite nilpotent groups as well. We also study the possibility of stable diagonalization of torsion matrices over imageG.