Groups, triality, and hyperquasigroups.
This paper is concerned with the algebraic structures known as hyperquasigroups, which are introduced as refinements of quasigroups. Hyperquasigroups were introduced to provide a more symmetrical approach to quasigroups, and a far-reaching implementation of triality. The aim of this paper is to establish comparable connections between hyperquasigroups and groups. The author introduces the key concept of the Cayley graph of a hyperquasigroup. According to the author within the Cayley graph provides a striking geometrical characterization of hyperquasigroups. The author focuses in the last two sections of the paper on the role of triality in hyperquasigroups, taking advantage of an orthant structure within the reflexion-inversion space to recover classical quasigroup information from a hyperquasigroup.
scientific article; zbMATH DE number 6043586
scientific article