Attestation committee
Accreditation committee
Expert committee
Dispositions, instructions
Normative acts
Nomenclature
Institutions
Scientific councils
Seminars
Theses
Scientific advisers
Scientists
Doctoral students
Postdoctoral students
CNAA logo

 română | русский | english


Commutative Moufang loops and CH-quasigroups with finiteness conditions"


Author: Gurdiş Aliona
Degree:doctor of physics and mathematics
Speciality: 01.01.06 - Mathematical logics, algebra and theory of numbers
Year:2010
Scientific adviser: Nicolae Sandu
doctor, associate professor (docent), Tiraspol State University
Scientific consultant: Vasile Ursu
doctor habilitat, associate professor (docent), Tiraspol State University
Institution: Tiraspol State University
Scientific council: DH 01-01.01.06
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Status

The thesis was presented on the 26 March, 2010
Approved by NCAA on the 3 June, 2010

Abstract

Adobe PDF document0.33 Mb / in romanian

Keywords

commutative Moufang loops (abbreviated CML), central nilpotent subloop, central soluble subloop, invariant (non-invariant) subloop, finite special rank, minimum condition, maximum condition, multiplication group of quasigroup, CH-quasigroup

Summary

The paper was drafted in Chisinau, in 2010, is written in Romanian and consists of introduction, 4 chapters, conclusions, 90 bibliography titles and 83 pages of main text. The obtained results are published in 10 scientific papers.

The thesis is dedicated to the study of: CML with minimum (resp. maximum or with finite special rank); CH-quasigroups with minimum (maxumum or finite special rank) condition for subquasigroups.

The objectives of the thesis are: in the CML to consider the relationship between the maximum (minimum or finite special rang) condition for subloops and the maximum minimum or finite special rang) condition for different systems of subloops, as well as different systems of subgroups of the multiplicative group; to consider the CH-quasigroups with a finite rank through different systems of subquasigroups of finite rank or different systems of subgroups of finite rank of the multiplicative group.

The following results were obtained in the thesis: for the CML it established the equivalence between the maximum condition for subloops and the maximum condition for different systems of subloops, as well as for different systems of subgroups of the multiplicative group; for the CML it established the equivalence of the finite rank condition and finite rank condition for different systems of subloops and for different systems of subgroups of the multiplicative group, listed above; for the CML it obtained such a criterion that the CML satisfies different finiteness conditions: minimum condition for subloops, maximum condition for subloops, of finite rank; for CH-quasigroups it established the equivalence of different finiteness conditions: minimum (maximum) condition for subquasigroups.