On the representation of lattices by subgroup lattices
\textit{P. M. Whitman} [Bull. Am. Math. Soc. 52, 507-522 (1946; Zbl 0060.06505)] proved that every lattice can be embedded in the subgroup lattice of a suitable group. In this paper the author studies the problem of embedding in lattices of subgroups of relatively free (i.e. free in a variety) groups. He proves that any lattice satisfying Whitman's condition can be embedded in the subgroup lattice of a free group of an arbitrary non-soluble group variety. Some interesting corollaries are examined.
scientific article; zbMATH DE number 1226192