Moody's induction theorem
Gerald H. Cliff, Alfred Weiss · Illinois Journal of Mathematics · 1988
FOR POLYCYCLIC BY FINITE GROUPS. The map from EGo(kF) to Go(kH), given by the sum of inductions from finite subgroups F of H, is surjective.To prove this, let H be a normal subgroup of H of smaller Hirsch length than H, such that H/HI F is abelian by finite, and write the group ring kH as a crossed product (kH), (H/Hx).Then use induction on the Hirsch length.Here is an outline of our proof of Moody's Theorem.Let A be a finitely generated free abelian normal subgroup of F of finite index, and let G denote