Reduction of UNil for finite groups with normal abelian Sylow 2-subgroup
Geometric Topology
2008-11-24 v4 Algebraic Topology
Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0609225,
title = {Reduction of UNil for finite groups with normal abelian Sylow 2-subgroup},
author = {Qayum Khan},
journal= {arXiv preprint arXiv:math/0609225},
year = {2008}
}
Comments
29 pages, revision of decorations, correction of Homological Reduction