A nilpotent group is a group 
for which the group
upper central series
 |
of the group terminates with 
for some 
.
Nilpotent groups have the property that each proper subgroup is properly contained in its normalizer. A finite nilpotent group is the group direct product of its Sylow p-subgroups.
A group has nilpotency class at most 2 when every commutator is central.
Su and Xia (2026) reported that, for every fixed prime number 
,
the proportion of isomorphism classes of groups of group order 
having nilpotency class 2 tends to
1 as 
.
They also reported that almost all finite groups,
counted by group order up to 
, have nilpotency class 2 and group
order 
,
where 
is the floor function. Su and Xia (2026) report
collaboration with GPT-6.
-Groups of Class Two." 8 Oct 2026. 