The group upper central series, also called the upper central sequence (Wuthrich 2016-2017), of a group 
is the ascending sequence of
normal subgroups
 |
that is constructed in the following way:
1. 
is the center of 
.
2. For 
,
is the unique subgroup of 
such that 
is the center of
.
If the group upper central series of a group terminates with 
for some 
,
then 
is called a nilpotent group.
