Open AccessSubsystems and Automorphisms of Some Finite Magmas of Order k + k2
Author(s) -
A. V. Litavrin
Publication year - 2020
Publication title -
izvestiâ saratovskogo universiteta. novaâ seriâ. seriâ matematika. mehanika. informatika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.255
H-Index - 4
eISSN - 2541-9005
pISSN - 1816-9791
DOI - 10.18500/1816-9791-2020-20-4-457-467
Subject(s) - automorphism , order (exchange) , permutation (music) , magma , permutation group , group (periodic table) , mathematics , idempotence , element (criminal law) , pure mathematics , class (philosophy) , set (abstract data type) , finite group , inner automorphism , automorphism group , algebra over a field , computer science , geology , physics , volcano , geochemistry , business , political science , artificial intelligence , law , acoustics , quantum mechanics , programming language , finance
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.