LATTICE UNIVERSALITY OF LOCALLY FINITE \(p\)-GROUPS

Vladimir B. Repnitskiǐ     (Ural Federal University, 19 Mira str., Ekaterinburg, 620002, Russian Federation)

Abstract


For an arbitrary prime \(p\), we prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite \(p\)-group. In particular, every lattice is embeddable in the subgroup lattice of a locally finite \(p\)-group.


Keywords


Subgroup lattice, Algebraic lattice, Complete sublattice, Lattice-universal class of algebras, Locally finite \(p\)-group, Group valuation.

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References


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DOI: http://dx.doi.org/10.15826/umj.2023.1.011

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