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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 19/2003

Sergei Evdokimov and Ilia Ponomarenko ##
A NEW LOOK AT THE BURNSIDE-SCHUR THEOREM

This preprint was accepted December 10, 2003

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.

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