| Abstrakt: |
Mark and Paupert devised a general method for obtaining presentations for arithmetic non-cocompact lattices, Γ , in isometry groups of negatively curved symmetric spaces. The method involves a classical theorem of Macbeath applied to a Γ -invariant covering by horoballs of the negatively curved symmetric space upon which Γ acts. In this paper, we will discuss the application of their method to the Picard modular groups, PU (2 , 1 ; O d) , when d = 2 , 11 , and obtain presentations for these groups, which completes the list of presentations for Picard modular groups whose entries lie in Euclidean domains, namely those with d = 1 , 2 , 3 , 7 , 11 . [ABSTRACT FROM AUTHOR] |
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