Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Litavrin A. V. Subsystems and Automorphisms of Some Finite Magmas of Order k + k2. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 4, pp. 457-467. DOI: 10.18500/1816-9791-2020-20-4-457-467, EDN: BVWMTL

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2020
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Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
512.54+512.57
DOI: 
10.18500/1816-9791-2020-20-4-457-467
EDN: 
BVWMTL

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

Autors: 
Litavrin Andrey Viktorovich, Siberian Federal University
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 > 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 > 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.

Key words: 
magma
groupoid
subsystems of magmas
automorphisms of groupoids
automorphisms of magmas
subgroupoids
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Received: 
01.09.2019
Accepted: 
30.09.2019
Published: 
30.11.2020
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