A group action 
might preserve a special kind of partition
of 
called a system of blocks. A block
is a subset 
of 
such that for any group element 
either
1. 
preserves 
, i.e., 
, or
2. 
translates everything in 
out of 
, i.e., 
.
For example, the general linear group 
acts on the plane minus the origin,
. The lines 
are blocks because either a line is mapped to itself,
or to another line. Of course, the points on the line may be rescaled, so the lines
in 
are minimal blocks.
In fact, if two blocks intersect then their intersection is also a block. Hence, the minimal blocks form a partition
of 
. It is important to avoid confusion
with the notion of a block in a block design, which
is different.
The concept of a fundamental domain generalizes that of a minimal group block.
