The upper central series of a group 
is the sequence of groups (each term normal in the term following
it)
 |
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 upper central series of a group terminates with 
for some 
, then 
is called a nilpotent group.
