Vol. 3, No. 4, 2009

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The structure of the group {\slshape\bfseries G}(\kern-.1emk\/[t\kern.1em]): Variations on a theme of Soulé

Benedictus Margaux

Vol. 3 (2009), No. 4, 393–409
Abstract

Following Soulé’s ideas from 1979, we give a presentation of the abstract group for any semisimple (connected) simply connected absolutely almost simple $k$-group . As an application, we give a description of in terms of direct limits, and show that the Whitehead group and the naive group of connected components of coincide.

Keywords
Bruhat–Tits buildings, arithmetic groups, simplicial fundamental domain
Primary: 20G10
Secondary: 20F05