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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Received: 18 April 2002 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 19D35, 16S35, 16H05.
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Kuku, A., Tang, G. Higher K-theory of group-rings of virtually infinite cyclic groups. Math. Ann. 325, 711–726 (2003). https://doi.org/10.1007/s00208-002-0397-2
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DOI: https://doi.org/10.1007/s00208-002-0397-2