Some amalgam structures for Bianchi groups

Abstract

Splittings as an amalgamated sum, where one of the factors is the projective elementary matrices, are displayed for all the Bianchi groups except for the Euclidian ones. Also splittings as an HNN group, where the base is PS L 2 ( Z ) {\text {PS}}{{\text {L}}_2}(Z) , are given for all the Bianchi groups except PS L 2 ( O 1 ) {\text {PS}}{{\text {L}}_2}({O_1}) and PS L 2 ( O 3 ) {\text {PS}}{{\text {L}}_2}({O_3}) .