title: Automorphisms of finite quasigroups with no subquasigroups
metadata.name: dc.contributor.author
metadata.value: Artamonov, Viacheslav A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-28T13:50:25Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-28T13:50:25Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Artamonov V.А. Automorphisms of finite quasigroups with no subquasigroups. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 2, pp. 197–209.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.202
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17927
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: It is shown that polynomially complete quasigroups with no subquasigroups are quasitermal.
  The case of transitive action of the automorphism group on these quasigroups is
  considered. In particular the case of quasigroup of a prime power order defined on arithmetic
  vector space over a finite field is considered in details. There are found some necessary
  conditions under which a multplication in this space given in terms of coordinates corresponds
  to a quasigroup. The case of the 2-element field is considered in detalis. In this
  case the quasigroup multiplication is given in terms of Boolean function. The is found a
  criteria for a quasigroup multiplication. Under some assumptions there are classified up to
  an isotopy all quasigroups of order 4 in terms of Boolean function. Polynomially complete
  quasigroups play a significant role because the problem of solutions of polynomial equation
  in them is NP-complete. This property is important for the securing information, since crypto-transformations are defined in terms of quasigroup operations. The same argument
  shows the importance of quasigroups with no proper subquasigroups.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported Russian-Indian project QGSEC.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: quasigroups
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: automorphism
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: permutations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Automorphisms of finite quasigroups with no subquasigroups
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 197-209.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17927/1/197-209.pdf
resources.format: Adobe PDF
resources.size: 327 kB