A group block for a group action 
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 punctured lines 
, where 
, are blocks because either
a line is mapped to itself, or to another line.
These punctured lines are not minimal blocks. Every singleton
is a block, and each punctured line contains positive rays, which are also blocks.
In fact, if two blocks intersect then their intersection is also a block. Hence, the minimal nonempty blocks under inclusion are singletons,
forming the singleton set partition of 
. It is important to avoid confusion with the notion of
a block in a block design, which is different.
A fundamental domain is instead defined by the orbits of the group action.
