A REDUCTION THEOREM FOR UNil OF FINITE GROUPS WITH NORMAL ABELIAN SYLOW 2-SUBGROUP

Let F be a finite group with a Sylow 2-subgroup S that is normal and abelian. Using hyperelementary induction and cartesian squares, we prove that Cappell’s unitary nilpotent groups UNil∗(Z[F ];Z[F ],Z[F ]) have an induced isomorphism to the quotient of UNil∗(Z[S];Z[S],Z[S]) by the action of the group F/S. In particular, any finite group F of odd order has the same UNil-groups as the trivial group. The broader scope is the study of the L 〈−∞〉 ∗ -theory of virtually cyclic groups, based on the Farrell-Jones isomorphism conjecture. Also, we obtain partial results on these UNil for special 2-groups.