The set of all zero-systems of a group 
is denoted 
and is called the block monoid of 
since it forms a commutative monoid under the operation of
zero-system addition defined by
 |
The monoid has identity 
,
the zero-system consisting of no elements.
For a nonempty subset 
of 
, 
is defined as the set of all zero-systems of 
containing only elements from 
. For any subset 
of 
,
is a commutative submonoid of 
. If context makes it obvious, 
is often omitted and 
is written.
A zero-system is minimal if it contains no proper zero-systems. The set 
is defined as the set of all minimal zero-systems of 
.
