Stably free modules over virtually free groups

Abstract

Let $F_m$ be the free group on $m$ generators and let $G$ be a finite nilpotent group of non square-free order; we show that for each $m\ge 2$ the integral group ring ${\bf Z}[G\times F_m]$ has infinitely many stably free modules of rank 1.Comment: 9 pages. The final publication is available at http://www.springerlink.com doi:10.1007/s00013-012-0432-

Stably free modules over rings of Laurent polynomials

“…O'Shea [11] has shown a similar result for the groups Z[F n × C p 2 ] when n ≥ 2 and p is prime. It is known (cf.…”