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A new proof of Whitman’s embedding theorem. (English) Zbl 0828.06004
In 1946 P. M. Whitman proved that every lattice can be embedded into a partition lattice. Since partition lattices can be embedded into subgroup lattices, it follows that every lattice is isomorphic to a sublattice of the subgroup lattice of a suitable group. The author gives a direct and relatively short proof of this result utilizing a basic construction of combinatorial group theory: the HNN-extension.

MSC:
06B15 Representation theory of lattices
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E15 Chains and lattices of subgroups, subnormal subgroups
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