Central product of UT(3,Z) and Z identifying center with 2Z
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This group can be defined in the following equivalent ways:
- It is the central product of unitriangular matrix group:UT(3,Z) and the group of integers where the subgroup of is identified with the center of .
- It is the following group of matrices under multiplication:
This group is almost like unitriangular matrix group:UT(3,Z). In fact, occurs as a subgroup of index two inside it. However, unlike , it is a CS-Baer Lie group, and hence can participate in the CS-Baer correspondence.