On quasivarieties of nilpotent Moufang loops. II

Vasile I. Ursu

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 3, page 491-499
  • ISSN: 0010-2628

Abstract

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In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.

How to cite

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Ursu, Vasile I.. "On quasivarieties of nilpotent Moufang loops. II." Commentationes Mathematicae Universitatis Carolinae 53.3 (2012): 491-499. <http://eudml.org/doc/246345>.

@article{Ursu2012,
abstract = {In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.},
author = {Ursu, Vasile I.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {basis; loop; associator; commutator; nilpotent; variety; quasivariety; quasivarieties of nilpotent Moufang loops; free Moufang loops; varieties of loops; associators; commutators; bases of quasiidentities; finite bases of identities; lattices of quasivarieties},
language = {eng},
number = {3},
pages = {491-499},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On quasivarieties of nilpotent Moufang loops. II},
url = {http://eudml.org/doc/246345},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Ursu, Vasile I.
TI - On quasivarieties of nilpotent Moufang loops. II
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 3
SP - 491
EP - 499
AB - In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.
LA - eng
KW - basis; loop; associator; commutator; nilpotent; variety; quasivariety; quasivarieties of nilpotent Moufang loops; free Moufang loops; varieties of loops; associators; commutators; bases of quasiidentities; finite bases of identities; lattices of quasivarieties
UR - http://eudml.org/doc/246345
ER -

References

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  1. Ol'shanskii A.Yu., Conditional identities in finite groups, Sibirsk. Mat. Zh. 15 (1974), no. 6, 1409–1413. Zbl0307.20017MR0367068
  2. Budkin A.I., 10.1007/BF01669499, Algebra i Logika 18 (1979), no. 2, 127–136. MR0566777DOI10.1007/BF01669499
  3. Ursu V.I., On quasiidentities of finitely generated commutative Moufang loops, Algebra i Logika 30, (1991), no. 6, 726–734. MR1213732
  4. Bruck R.H., A Survey of Binary Systems, Springer, Berlin-Heidelberg-New York, 1958. Zbl0141.01401MR0093552
  5. Kargapolov M.I., Merzlyakov Yu.I., Fundamentals of Group Theory, Moscow, Nauka, 1982. Zbl0884.20001MR0677282
  6. Dlab V., Kořínek V., The Frattini subgroup of a direct product of groups, Czechoslovak Math. J. 10 (1960), 50–358. Zbl0101.26303MR0114858
  7. Mal'cev A.I., Algebraic Systems, Moscow, Nauka, 1970. Zbl0223.08001MR0282908
  8. Vinogradov A.A., Quasivarieties of Abelian groups, Algebra i Logika Sem. 4 (1965), no. 6, 15–18. MR0199262
  9. Ursu V.I., On identities of nilpotent Moufang loops, Rev. Roumaine Math. Pures Appl. 45 (2000), no. 3, 537–548. Zbl0993.20043MR1840173

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