Abstract
The paper is devoted to the theory of singly generated multivalued groups. We construct new classes of such groups and find criteria that allow to check whether such a group is a coset group. For this purpose, we introduce the construction of a σ-extension of a singly generated multivalued group with Hermitian generator. This construction is based on the relation of the theory of such groups with the theory of symmetric graphs. The main result of the paper is as follows: the suggested construction of σ-extensions of singly generated bicoset multivalued groups with Hermitian generators is equivariant with respect to morphisms of graph-theoretic nature. Bibliography: 11 titles.
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