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

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.