Multi-groups | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2024. № 87. DOI: 10.17223/19988621/87/4

Multi-groups

In the present paper we define homogeneous algebraic systems. Particular cases of these systems are semigroup (monoid, group) systems. These algebraic systems were studied by J. Loday, A. Zhuchok, T. Pirashvili, and N. Koreshkov. Quandle systems were introduced and studied by V. Bardakov, D. Fedoseev, and V. Turaev. We construct some group systems on the set of square matrices over a field k. Also, we define rack systems on the set V x G , where V is a vector space of dimension n over k and G is a subgroup of GLn(k). Finally, we find the connection between skew braces and dimonoids.

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Keywords

algebraic system, homogeneous algebraic system, groupoid, semigroup, monoid, group, semigroup system, quandle system, dimonoid, skew brace, multi-group, multi-quandle

Authors

Name	Organization	E-mail
Kozlovskaya Tatyana A.	Tomsk State University	t.kozlovskaya@math.tsu.ru

Всего: 1

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