Abstract: We present the following constructions of extending a trivial quandle by a group with a nontrivial abelian subgroup, a quandle over a noncommutative group by an arbitrary antiautomorphism, a quandle presenting from a generalized Alexander quandle with the replacement of the automorphism by a central antiautomorphism, and a quandle over an n-dimensional module depending on n(n 1) 1 parameters with n 2 in a commutative unital ring. Also we study bijections of some groups which are commute with inner automorphisms. The work was supported by the Fundamental Research Program of the Siberian Branch of the Russian Academy of Sciences (no. I.1.5, Project FWNF2022-0009). Simonov A.A., Neshchadim M.V. and Borodin A.N. CONSTRUCTIONS OF QUANDLES OVER GROUPS AND RINGS. Siberian Mathematical Journal, 2024, Vol. 65, No. 3.

Cite: Neshchadim M.
CONSTRUCTIONS OF QUANDLES OVER GROUPS AND RINGS AND SOME QUESTIONS OF GROUP THEORY
5th International Conference GROUPS AND QUANDLES IN LOW-DIMENSIONAL TOPOLOGY 13-15 Jun 2024