Let be a cyclic monoid of order n, that is, .

A finite abelian group of order n has exactly n distinct characters.

Note that isometries of order n include, but are not restricted to, n-fold rotations.

The complexity is therefore reduced to one of order n, rather than n.

In general, a T-hexagon of order n has triangles.

For every positive integer n, most groups of order n are solvable.

More precisely, for every finite group G of order n, the following statements are equivalent:

Hypercube graphs of order n are known to be a Lévy family.

Some numbers n are such that every group of order n is cyclic.

The symmetric group on a set of n elements has order n!