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 Zap. Nauchn. Sem. POMI, 2010, Volume 378, Pages 184–227 (Mi znsl3834)

Duality in the theory of finite commutative multivalued groups

P. V. Yagodovsky

Finance Academy under the Government of the Russian Federation, Moscow, Russia

Abstract: The purpose of this paper is to construct a duality theory for finite commutative multivalued groups and to demonstrate its connection with the classical duality in the theory of ordinary groups and the Kawada–Delsarte duality in algebraic combinatorics. We study in detail the case of multivalued groups of order three, construct a parameterization of the set of these groups, and obtain explicit formulas for the duality. In future, we plan to use this duality in the study of the coset problem. Bibl. 26 titles.

Key words and phrases: $n$-valued groups, coset and double coset groups, involutive multivalued groups, singly generated multivalued groups, association schemes, $C$-algebras, duality for multivalued groups, duality for $C$-algebras.

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English version:
Journal of Mathematical Sciences (New York), 2011, 174:1, 97–119

UDC: 515.179

Citation: P. V. Yagodovsky, “Duality in the theory of finite commutative multivalued groups”, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Zap. Nauchn. Sem. POMI, 378, POMI, St. Petersburg, 2010, 184–227; J. Math. Sci. (N. Y.), 174:1 (2011), 97–119

Citation in format AMSBIB
\Bibitem{Yag10} \by P.~V.~Yagodovsky \paper Duality in the theory of finite commutative multivalued groups \inbook Representation theory, dynamical systems, combinatorial methods. Part~XVIII \serial Zap. Nauchn. Sem. POMI \yr 2010 \vol 378 \pages 184--227 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl3834} \transl \jour J. Math. Sci. (N. Y.) \yr 2011 \vol 174 \issue 1 \pages 97--119 \crossref{https://doi.org/10.1007/s10958-011-0284-z} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952814287}