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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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A quandle is a well-known algebraic object, which has deep connection with knot theory. Qunadles were extensively used for knot invariants construction. Furthermore, certain generalizations of quandles, such as G-families of quandles due to A.Ishii, were successfully used to distguish knotted handlebodies and knotted trivalent graphs. In the present talk we will present a construction of multiplication of quandles defined on the same set Q. Under certain conditions on quandle operations, the resulting quandle product is also a quandle. This procedure allows one to construct families and groups of quandles, giving, for example, a natural interpretation of involutive quandles n-quandles. If time permits, we will also briefly discuss possible generalizations of Ishii construction of G- families of quandles and their applications to handlebody-knot theory. The talk is based on a joint work with V.G. Bardakov. The work was partially supported by RSF grant 21-11-00355.