A new look at the Burnside-Schur theorem
Group Theory
2007-05-23 v1 Combinatorics
Abstract
The famous Burnside-Schur theorem states that every primitive finite permutation group containing a regular cyclic subgroup is either 2-transitive or isomorphic to a subgroup of a 1-dimensional affine group of prime degree. It is known that this theorem can be expressed as a statement on Schur rings over a finite cyclic group. Generalizing the latters we introduce Schur rings over a finite commutative ring and prove an analog of this statement for them. Besides, the finite local commutative rings are characterized in the permutation group terms.
Cite
@article{arxiv.math/0310373,
title = {A new look at the Burnside-Schur theorem},
author = {Sergei Evdokimov and Ilia Ponomarenko},
journal= {arXiv preprint arXiv:math/0310373},
year = {2007}
}