Reduction of UNil for finite groups with normal abelian Sylow 2-subgroup

Details Reduction of UNil for finite groups with normal abelian Sylow 2-subgroup Reduction of UNil for finite groups with normal abelian Sylow 2-subgroup

2006-09-08

arxiv.org/abs/math/0609225v4

Journal of Pure and Applied Algebra, Volume 213, Number 3 (2009), 279--298

Mathematics

Geometric Topology

29 pages, revision of decorations, correction of Homological Reduction

Scientific paper

10.1016/j.jpaa.2008.07.005

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. We obtain partial information on these UNil when S is a finite abelian 2-group and when S is a special 2-group.

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