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Litavrin A. V. Subsystems and Automorphisms of Some Finite Magmas of Order k + k2. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2020, vol. 20, iss. 4, pp. 457-467. DOI: 10.18500/1816-9791-2020-20-4-457-467

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

Litavrin Andrey Viktorovich, Siberian Federal University

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.

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