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  • 1
    Electronic Resource
    Electronic Resource
    A local-global principle for finiteness properties ofS-arithmetic groups over number fields (1997)
    Springer
    Transformation groups 2 (1997), S. 215-223 
    Details
    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the preceding paper [AT] compactness propertiesC n andCP n for locally compact groups were introduced. They generalize the finiteness propertiesF n andFP n for discrete groups. In this paper a local-global principle forS-arithmetic groups over number fields is proved. TheS-arithmetic group г is of typeF n , resp.FP n , if and only if for allp inS thep-adic completionG p of the corresponding algebraic groupG is of typeC n resp.CP n . As a corollary we obtain an easy proof of a theorem of Borel and Serre: AnS-arithmetic subgroup of a semisimple group has all the finiteness propertiesF n .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01235942
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  • 2
    Electronic Resource
    Electronic Resource
    Compactness properties of locally compact groups (1997)
    Springer
    Transformation groups 2 (1997), S. 119-135 
    Details
    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Compactness propertiesC n andC P n for locally compact groupsG are introduced generalizing the finiteness propertiesF n andF P n for discrete groups. The propertyC 1 resp.C 2 is equivalent withG having a compact set of generators, resp. having a compact presentation. Some basic properties of the compactness propertiesC n are shown. A local-global principle is proved by the second named author in the adjacent paper of this volume.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01235936
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