Geodesic
On the separability problem for circulant S-rings
Algebra i analiz, Tome 28 (2016) no. 1, pp. 32-51.

Voir la notice de l'article provenant de la source Math-Net.Ru

A Schur ring (S-ring) over a group $G$ is said to be separable if every of its similaritities is induced by an isomorphism. A criterion is established for an S-ring to be separable in the case where the group $G$ is cyclic. Using this criterion, it is proved that any S-ring over a cyclic $p$-group is separable and that the class of separable circulant S-rings is closed with respect to duality.
Keywords: Shur ring, Cayley isomorphism, Cayley graph, circulant S-ring. 
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S. Evdokimov; I. Ponomarenko. On the separability problem for circulant S-rings. Algebra i analiz, Tome 28 (2016) no. 1, pp. 32-51. http://geodesic.mathdoc.fr/item/AA_2016_28_1_a1/

[1] Evdokimov S. A., Ponomarenko I. N., “Ob odnom semeistve kolets Shura nad konechnoi tsiklicheskoi gruppoi”, Algebra i analiz, 13:3 (2003), 139–154 | MR | Zbl

[2] Evdokimov S. A., Ponomarenko I. N., “Kharakterizatsiya tsiklotomicheskikh skhem i normalnye koltsa Shura nad tsiklicheskoi gruppoi”, Algebra i analiz, 14:2 (2002), 11–55 | MR | Zbl

[3] Evdokimov S. A., Ponomarenko I. N., “Raspoznavanie i proverka izomorfizma tsirkulyantnykh grafov za polinomialnoe vremya”, Algebra i analiz, 15:6 (2003), 1–34 | MR | Zbl

[4] Evdokimov S., Ponomarenko I., “Permutation group approach to association schemes”, European J. Combin., 30:6 (2009), 1456–1476 | DOI | MR | Zbl

[5] Evdokimov S. A., Ponomarenko I. N., “Shurovost S-kolets nad tsiklicheskoi gruppoi i obobschennoe spletenie grupp perestanovok”, Algebra i analiz, 24:3 (2012), 84–127 | MR | Zbl

[6] Evdokimov S., Kovács I., Ponomarenko I., “Characterization of cyclic Schur groups”, Algebra i analiz, 25:5 (2013), 61–85 | MR | Zbl

[7] Evdokimov S., Kovács I., Ponomarenko I., “On schurity of finite abelian groups”, Comm. Algebra, 44:1 (2016), 101–117 | DOI | MR | Zbl

[8] Evdokimov S., Ponomarenko I., “Coset closure of a circulant S-ring and schurity problem”, J. Algebra Appl., 15:4 (2016), 1650068 | DOI | MR | Zbl

[9] Muzychuk M., “On the structure of basic sets of Schur rings over cyclic groups”, J. Algebra, 169:6 (1994), 655–678 | DOI | MR | Zbl