On quasivarieties of nilpotent Moufang loops. I

Previous | Up | Next

Article

On quasivarieties of nilpotent Moufang loops. I. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 53 (2012), issue 3, pp. 475-489

MSC: 20N05 | MR 3017844 | Zbl 1257.20071

Keywords:
loop; associator; commutator; nilpotent; quasivarieties; quasiidentities; identities

Summary:
In this part the smallest non-abelian quasivarieties for nilpotent Moufang loops are described.

References:

[1] Mal'cev A.I.: On the inclusion of associative systems in groups, I. Mat. Sbornik 6 (1939), no. 2, 331–336. MR 0002152

[2] Mal'cev A.I.: On the inclusion of associative systems in groups, II. Mat. Sbornik 8 (1940), no. 2, 251–263. MR 0003420

[3] Mal'cev A.I.: Quasiprimitive classes of abstract algebras. Dokl. Akad. Nauk SSSR (N.S.) 108 (1956), 187–189. MR 0079572

[4] Mal'cev A.I.: Several remarks on quasivarieties of algebraic systems. Algebra i Logika Sem. 5 (1966), no. 3, 3–9. MR 0205902

[5] Mal'cev A. I.: Some borderline problems of algebra and logic. 1968 Proc. Internat. Congr. Math. (Moscow, 1966), pp. 217–231. MR 0233751

[6] Mal'cev A.I.: Algebraic Systems. Moscow, Nauka, 1970. MR 0282908 | Zbl 0223.08001

[7] Ursu V.I.: On identities of nilpotent Moufang loops. Rev. Roumaine Math. Pures Appl. 45 (2000), no. 3, 537–548. MR 1840173 | Zbl 0993.20043

[8] Bruck R.H.: A Survey of Binary Systems. Springer, Berlin-Heidelberg-New York, 1958. MR 0093552 | Zbl 0141.01401

[9] Koval'ski A.V., Ursu V.I.: An equational theory for a nilpotent A-loop. Algebra Logika 49 (2010), no. 4, 479–497. MR 2790173

[10] Kargapolov M.I., Merzlyakov Yu.I.: Fundamentals of Group Theory. Moscow, Nauka, 1982. MR 0677282 | Zbl 0884.20001

Partner of