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A Description of Subrings in \( V\left( {S_{p_1 } \times S_{p_2 } \times \cdots \times S_{p_m } } \right)\)

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Investigations in Algebraic Theory of Combinatorial Objects

Part of the book series: Mathematics and Its Applications ((MASS,volume 84))

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Abstract

The construction of V-rings of permutation groups and a description of their subrings are very important in the development of permutation group theory as well as combinatorics and graph theory. One can see about these connections in [1,3,6].

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References

  1. I.A. Faradžev, M.H. Klin, M.E. Muzichuk, Cellular rings and groups of automorphisms of graphs. [In this volume].

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  2. V.Z. Feinberg, The wreath product of permutation groups over partially ordered sets and filtres. Izv. AN BSSR (1971), 28–38 [In Russian].

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  3. A.A. Ivanov, M.H. Klin, I.A. Faradžev,Primitive representations of the nonabelian simple groups of order less than 106. Part 2. Preprint, Moscow, VNIISI, 1984 [In Russian].

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  4. L.A. Kalužnin, M.H. Klin, On certain maximal subgroups of symmetric and alternating groups, Mat. USSR Sb. 16 (1972), 95–123.

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  5. M.H. Klin, R. Pöschel, The König problem, the isomorphism problem for cyclic graphs and the method of Schur rings. - Colloq. Math. J. Bolyai, 25 Algebraic methods in graph theory, Szeged, 1978; North Holland Amsterdam 1981, pp. 405434.

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  6. B. Weisfeiler (edited by), On construction and identification of graphs. Lect. Notes Math., 1976, v.558.

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  7. H. Wielandt, Finite permutation groups. Academic Press, 1964.

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© 1994 Springer Science+Business Media Dordrecht

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Gol’fand, J.J. (1994). A Description of Subrings in \( V\left( {S_{p_1 } \times S_{p_2 } \times \cdots \times S_{p_m } } \right)\) . In: Faradžev, I.A., Ivanov, A.A., Klin, M.H., Woldar, A.J. (eds) Investigations in Algebraic Theory of Combinatorial Objects. Mathematics and Its Applications, vol 84. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1972-8_5

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  • DOI: https://doi.org/10.1007/978-94-017-1972-8_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4195-1

  • Online ISBN: 978-94-017-1972-8

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