He continues to research into permutation groups and model theory.

Some unusual rank-3 permutation groups (many from ) are listed below.

Inspired by this they decided to check for other rank 3 permutation groups on 100 points.

They are all subgroups of M, which is a permutation group on 24 points.

Lagrange also contributed in 1771 with his work on permutation groups.

Thus, for the permutation group G we will now write:

More formally, let G be a permutation group of order m and degree n.

There are several advantages to the modern approach over the permutation group approach.

Its homography group is the permutation group on these three.

Let be a finite permutation group acting on a set .

The first class of groups to undergo a systematic study was permutation groups.

Then the full symmetry need only contain the permutation group of spacetime events.

The primitive rank 3 permutation groups are all in one of the following classes:

Several 3-transposition groups are rank-3 permutation groups (in the action on transpositions).

Several of the sporadic simple groups were discovered as rank 3 permutation groups.

A transformation monoid whose elements are invertible is a permutation group.

A subgroup of a symmetric group is called a permutation group.

In many cases, the structure of a permutation group can be studied using the properties of its action on the corresponding set.

Thus, the cycle index of this permutation group is:

The Rubik's Cube puzzle is another example of a permutation group.

This is the semigroup anologue of a permutation group.

Formerly, when mathematicians spoke of "groups", they had meant permutation groups.

The simplest case, and the context in which the idea was first noticed, is that of finite groups (see primitive permutation group).

Bertrand's postulate was proposed for applications to permutation groups.

Earlier proofs had been for permutation groups.