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Article

Tůma, Jiří
Representing lattices by homotopy groups of graphs. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 40 (1999), issue 2, pp. 215-221
MSC: 06B15, 20E05, 20E15 | MR 1732642 | Zbl 0977.06003
Keywords:
subgroup lattice; lattice embedding; free group; homotopy group
Summary:
In this paper we represent every lattice by subgroups of free groups using the concept of the homotopy group of a graph.
References:
[Tů1] Tůma J.: On infinite partition representations and their finite quotients. Czech. Math. J. 45 (1995), 21-38. MR 1314529
[Tů2] Tůma J.: A new proof of Whitman's embedding theorem. J. Algebra 173 (1995), 459-462. MR 1325785 | Zbl 0828.06004
[W] Whitman P.: Lattices, equivalence relations, and subgroups. Bull. Amer. Math. Soc. 52 (1946), 507-522. MR 0016750 | Zbl 0060.06505
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