This criterion can for example be used to show that all the symmetric groups are realizable.

Among other things, this ring plays an important role in the representation theory of the symmetric groups.

The smallest example is the symmetric group on 3 points, with 6 elements.

The symmetric group on three points has Fitting length 2.

The symmetric group on four points has Fitting length 3.

This is the symmetric group, also sometimes called the composition group.

They play an important role in the representation theory of the symmetric group.

Robinson specialized in the study of the symmetric groups on which he became a recognized authority.

He wrote some forty papers on the topic of symmetric groups.

The symmetric group on n-letters, S, may be described as follows.