Varieties of \(\ell\)-groups with the identity \([x^ p,y^ p]=e\) have finite bases. (English. Russian original) Zbl 0544.06013
Algebra Logic 23, 20-35 (1984); translation from Algebra Logika 23, No. 1, 27-47 (1984).
Let p be a prime. Let us denote by \({\mathcal L}_ p\) the variety of lattice ordered groups defined by the identity \([x^ p,y^ p]=e\). This paper contains the following two main results: 1) All proper subvarieties of the variety \({\mathcal L}_ p\) are constructively described. 2) It is proved that each subvariety of \({\mathcal L}_ p\) possesses a finite basis of identities.
Reviewer: J.Jakubík
MSC:
| 06F15 | Ordered groups |
| 20F60 | Ordered groups (group-theoretic aspects) |
| 08B15 | Lattices of varieties |
| 20E10 | Quasivarieties and varieties of groups |
| 06B20 | Varieties of lattices |
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