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CNAA / Theses / 2018 / June /

Commutative Loops Moufang with finiteness conditions


Author: Lupașco Natalia
Degree:doctor of
Speciality: 01.01.06 - Mathematical logics, algebra and theory of numbers
Year:2018
Scientific adviser: Nicolae Sandu
doctor, Tiraspol State University
Scientific consultant: Liubomir Chiriac
doctor habilitat, professor, Tiraspol State University
Institution: Tiraspol State University

Status

The thesis was presented on the 26 June, 2018
Approved by NCAA on the 23 November, 2018

Abstract

Adobe PDF document – 0.34 Mb / in romanian

Thesis

CZU 512.548(043.3)

Adobe PDF document 2.23 Mb / in romanian
112 pages

Keywords

commutative loop Moufang(CLM), finiteness conditions, group of automorphism, semigroup of endomorphisms

Summary

Thesis structure: the thesis is written in Romanian and contains introduction, 4 chapter, conclusions, 113 references, 111 pages of basic text. The main result of the thesis was published in 12 scientific works.

Field of study of the thesis: CLM with finiteness conditions.

Thesis aim and objectives: establishing the condition for which the commutative Moufang loop is the central nilpotent (of the given class); describing the group F(1) of the commutative Moufang loop which is approximate with commutative Moufang central nilpotence loops; determining the group of automorphism of commutative Moufang loop with minimal conditions; determining the structure of commutative Moufang loop which admit decomposition in the lower central series; determining the structure of meta-hamiltonian commutative Moufang loops.

Scientific innovation and originality:The main results of the paper are new. Thus, there have been established the condition for which the commutative Moufang loop is the central nilpotent (of the given class); there have been described the group F(1) of the commutative Moufang loop which is approximate with commutative Moufang central nilpotence loops; there have been determined the group of automorphism of commutative Moufang loop with minimal conditions; there have been determined the structure of commutative Moufang loop which admit decomposition in the lower central series; there have been determined the structure of meta-hamiltonian commutative Moufang loops.

The important scientific problem solved: consists in the description proprieties of commutative Moufang loops and identifying their connection to the multiplicative group and the groups of automorphisms in order to determine the structure of commutative Moufang loops with finiteness conditions.

The theoretical significance and applicative value of the thesis: there have been elaborated the new concepts, methods and new constructions which contributed to achieving goals and objectives of the research. The basic research of the work are new. The methodology applied in work allowed to find the solution of concrete problems of the theory of CLM. The implementation of the scientific results: the results from this work can be used in the theory of quasigroups and loops, in cryptography and in elaborating teaching courses.