Normal cyclotomic schemes over a finite commutative ring
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S. Evdokimov and I. Ponomarenko
Translated by: the authors - St. Petersburg Math. J. 19 (2008), 911-929
- DOI: https://doi.org/10.1090/S1061-0022-08-01027-3
- Published electronically: August 21, 2008
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Abstract:
Cyclotomic association schemes over a finite commutative ring $R$ with identity are studied. The main goal is to identify the normal cyclotomic schemes $\mathcal {C}$, i.e., those for which $\operatorname {Aut}(\mathcal {C})\le A\Gamma L_1(R)$. The problem reduces to the case where the ring $R$ is local, and in this case a necessary condition of normality in terms of the subgroup of $R^\times$ that determines $\mathcal {C}$ is given. This condition is proved to be sufficient for a large class of local rings including the Galois rings of odd characteristic.References
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Bibliographic Information
- S. Evdokimov
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Email: evdokim@pdmi.ras.ru
- I. Ponomarenko
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Email: inp@pdmi.ras.ru
- Received by editor(s): June 20, 2007
- Published electronically: August 21, 2008
- Additional Notes: Partially supported by RFBR (grants nos. 07-01-00485, 05-01-00899, and 06-01-00471), and by NSH (grant no. 4329.2006.1)
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 911-929
- MSC (2000): Primary 13M99
- DOI: https://doi.org/10.1090/S1061-0022-08-01027-3
- MathSciNet review: 2411639
Dedicated: To the centenary of the birth of D. K. Faddeev