Schurity of rings over a cyclic group and generalized wreath product of permutation groups
Authors:
S. A. Evdokimov and I. N. Ponomarenko
Translated by:
the authors
Original publication:
Algebra i Analiz, tom 24 (2012), nomer 3.
Journal:
St. Petersburg Math. J. 24 (2013), 431460
MSC (2010):
Primary 20E22; Secondary 20J05
Published electronically:
March 21, 2013
MathSciNet review:
3014128
Fulltext PDF
Abstract 
References 
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Additional Information
Abstract: With the help of the generalized wreath product of permutation groups introduced in the paper, the automorphism group of an ring over a finite cyclic group is studied. Criteria for the generalized wreath product of two such rings to be Schurian or nonSchurian are proved. As a byproduct, it is shown that the group is a Schur one (i.e., any ring over it is Schurian) whenever the total number of prime factors of the integer does not exceed . Moreover, the structure of a nonSchurian ring over is described in the case where . In particular, the last result implies that if , where and are primes, then is a Schur group.
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Additional Information
S. A. Evdokimov
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, Saint Petersburg 191023, Russia
Email:
evdokim@pdmi.ras.ru
I. N. Ponomarenko
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, Saint Petersburg 191023, Russia
Email:
inp@pdmi.ras.ru
DOI:
http://dx.doi.org/10.1090/S106100222013012465
Keywords:
Shurian ring,
generalized wreath product,
permutation group
Received by editor(s):
April 7, 2011
Published electronically:
March 21, 2013
Additional Notes:
Partially supported by the Slovenian–Russian bilateral project (grant nos. BIRU/1011018 and BIRU/1213035). The second author was also supported by RFBR (grant no. 110100760a)
Article copyright:
© Copyright 2013
American Mathematical Society
