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

Aderemi O. Kuku | Zendy; Guoping Tang | Zendy

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

Author(s) -

Aderemi O. Kuku,

Guoping Tang

Publication year - 2003

Publication title -

mathematische annalen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.235

H-Index - 75

eISSN - 1432-1807

pISSN - 0025-5831

DOI - 10.1007/s00208-002-0397-2

Subject(s) - mathematics , epimorphism , dihedral group , cyclic group , group (periodic table) , combinatorics , kernel (algebra) , finite group , pure mathematics , algebraic number , group theory , discrete mathematics , mathematical analysis , abelian group , chemistry , organic chemistry

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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