Unitriangular matrix group:UT(3,Q)

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VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

The group described here is the unitriangular matrix group of degree three over the field of rational numbers $\mathbb{Q}$.

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