TORSION UNITS IN INFINITE GROUP-RINGS

A conjecture of Zassenhaus says that if G is a finite group then any unit u = SIGMA u(g) g of finite order in ZG is conjugate in QG to +/- g, for some g is-an-element-of G. This is known to be equivalent to saying that u(g0) = SIGMA(h approximately g0), u(h) is nonzero for a unique conjugacy class C(g0) 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 ZG. (C) 1994 Academic Press, Inc.