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A NEW LOOK AT THE BURNSIDE–SCHUR THEOREM

Published online by Cambridge University Press:  02 August 2005

SERGEI EVDOKIMOV  and
ILIA PONOMARENKO
SERGEI EVDOKIMOV
Affiliation:
Russian Academy of Sciences, St. Petersburg Institute for Informatics and Automation, 14th line 39, St Petersburg, 199178, [email protected]
ILIA PONOMARENKO
Affiliation:
Russian Academy of Sciences, St Petersburg Department of V. A. Steklov Institute of Mathematics, 27, Fontanka, St Petersburg, 191023, [email protected]
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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 latter, Schur rings are introduced over a finite commutative ring, and an analogue of this statement is proved for them. Also, the finite local commutative rings are characterized in permutation group terms.

Keywords

20B1020B1505E99
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 4 , August 2005 , pp. 535 - 546
Copyright
© The London Mathematical Society 2005

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