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Higher K -theory of group-rings of virtually infinite cyclic groups

Mathematische Annalen (Impact Factor: 1.38). 03/2003; 325(4):711-726. DOI: 10.1007/s00208-002-0397-2

ABSTRACT  F.T. Farrell and L.E. Jones conjectured in [7] that Algebraic K-theory of virtually cyclic subgroups V should constitute `building blocks' for the Algebraic K-theory of an arbitrary group G. In [6], they obtained some results on lower K-theory of V. In this paper, we obtain results on higher K-theory of virtually infinite cyclic groups V in the two cases: (i) when V admits an epimorphism (with finite kernel) to the infinite cyclic group (see 2.1 and 2.2(a),(b)) and (ii) when V admits an epimorphism (with finite kernel) to the infinite dihedral group (see 3.1, 3.2, 3.3).

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