Subsystems and Automorphisms of Some Finite Magmas of Order k + k2

Abstract

This work is devoted to the study of subsystems of some finite magmas S = (V,*) with a generating set of k elements and order k + k2. For k more than 1, the magmas S are not semigroups and quasigroups. An element-by-element description of all magmas S subsystems is given. It was found that all the magmas S have subsystems that are semigroups. For k more than 1, subsystems that are idempotent nonunit semigroups are explicitly indicated. Previously, a description of an automorphism group was obtained for magmas S. In particular, every symmetric permutation group Sk is isomorphic to the group of all automorphisms of a suitable magma S. In this paper, a general form of automorphism for a wider class of finite magmas of order k + k2 is obtained.

Keywords

• magma
• groupoid
• subsystems of magmas
• automorphisms of groupoids
• automorphisms of magmas
• subgroupoids