Non-Finiteness Results for Nil-Groups

Generalizing an idea of Farrell we prove that for a ring ƒ and a ring automorphism ˛ of finite order the groups Nil0.ƒI ˛ / and all of its p–primary subgroups are either trivial or not finitely generated as an abelian group. We also prove that if ˇ and are ring automorphisms such that ˇ ı is of finite order then Nil0.ƒI ƒˇ; ƒ / and all of its p–primary subgroups are either trivial or not finitely generated as an abelian group. These Nil-groups include the Nil-groups appearing in the decomposition of Ki of virtually cyclic groups for i 1. 18F25; 19B28, 19D35