an:00056977
Zbl 0755.06010
Gurchenkov, S. A.
On three questions in the theory of l-varieties
RU
Czech. Math. J. 41(116), No. 3, 405-410 (1991).
00007305
1991
j
06F15
variety of lattice-ordered groups; divisible \(\ell\)-group; nilpotent \(\ell\)-groups; divisible varieties; rigid \(\ell\)-groups
A variety of lattice-ordered groups \(\mathcal V\) is called divisible if every \(\ell\)-group \(G\) in \(\mathcal V\) can be embedded as an \(\ell\)-subgroup in a divisible \(\ell\)-group \(G^*\) in \(\mathcal V\). The main results of the paper are: There is a continuum of non-divisible varieties of nilpotent \(\ell\)- groups. There is a continuum of divisible varieties of nilpotent \(\ell\)- groups. The variety of rigid \(\ell\)-groups has basis rank 2.
J.Rach??nek (Olomouc)