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.