Article
Keywords:
basis; loop; associator; commutator; nilpotent; variety; quasivariety
Summary:
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.
References:
[1] Ol'shanskii A.Yu.:
Conditional identities in finite groups. Sibirsk. Mat. Zh. 15 (1974), no. 6, 1409–1413.
MR 0367068 |
Zbl 0307.20017
[2] Budkin A.I.:
Quasiidentities of nilpotent groups and groups with one relation. Algebra i Logika 18 (1979), no. 2, 127–136.
DOI 10.1007/BF01669499 |
MR 0566777
[3] Ursu V.I.:
On quasiidentities of finitely generated commutative Moufang loops. Algebra i Logika 30, (1991), no. 6, 726–734.
MR 1213732
[6] Dlab V., Kořínek V.:
The Frattini subgroup of a direct product of groups. Czechoslovak Math. J. 10 (1960), 50–358.
MR 0114858 |
Zbl 0101.26303
[8] Vinogradov A.A.:
Quasivarieties of Abelian groups. Algebra i Logika Sem. 4 (1965), no. 6, 15–18.
MR 0199262
[9] 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