Central product of UT(3,Z) and Q
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Definition
This group is defined as an external central product of unitriangular matrix group:UT(3,Z) with the group of rational numbers , where we identify the full center of the first group with the subgroup
in the latter (see Z in Q).
Arithmetic functions
Function | Value | Similar groups | Explanation |
---|---|---|---|
order | countably infinite | ||
exponent | infinite (elements of infinite order) | ||
nilpotency class | 2 | ||
derived length | 2 |
Group properties
Property | Meaning | Satisfied? | Explanation | Comment |
---|---|---|---|---|
abelian group | any two elements commute | No | ||
group of nilpotency class two | Yes | |||
metabelian group | Yes | |||
torsion-free group | Yes |