The normal subgroup lattice of 2-transitive automorphism groups of linearly ordered sets (Q1069960)

An infinite linearly ordered set, or briefly infinite chain, (\(\Omega\),\(\leq)\) is called doubly homogeneous if its automorphism group A(\(\Omega)\) acts 2-transitively on the set \(\Omega\). The author investigates the lattice N(A(\(\Omega)\)) of all normal subgroups of A(\(\Omega)\) using combinatorial and model-theoretic means. Certain natural sublattices of N(A(\(\Omega)\)) are shown to be Stone algebras, and several first order properties of their dense and dually dense elements are characterized within the Dedekind-completion of (\(\Omega\),\(\leq)\). As consequences, various group- and lattice-theoretic results follow from this.