On the representation of lattices by subgroup lattices (Q1272088)
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scientific article; zbMATH DE number 1226192
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the representation of lattices by subgroup lattices |
scientific article; zbMATH DE number 1226192 |
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On the representation of lattices by subgroup lattices (English)
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23 November 1998
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\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.
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lattice
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embedding
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subgroup lattice
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