Humphreys, J.J.A.M.; (2005) Algebraic properties of semi-simple lattices and related groups. Doctoral thesis , University of London.

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Abstract

Two abstract theories are developed. The first concerns isomorphism in variants with the same multiplicative properties as the Euler characteristic. It is used to show that the index of a subgroup in a semi-simple lattice is deter mined by its isomorphism type when that index is finite. This is also proved to be the case for subgroups of finite index in free products of finitely many semi-simple lattices as well as certain non-trivial extensions of Z by surface groups. In addition, a criterion for the failure of this property is given which applies to a large class of central extensions. The second development concerns the syzygies of groups. The results of this theory are used to define the cohomology groups of a duality group in terms of morphisms between stable modules in the derived category. The Farrell cohomology of virtual duality groups is also considered.

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