Abstract
Using combinatorial and model-theoretic means, we examine the structure of normal subgroup lattices N(A(Ω)) of 2-transitive automorphism groups A(Ω) of infinite linearly ordered sets (Ω, ≤). Certain natural sublattices of N(A(Ω)) are shown to be Stone algebras, and several first order properties of their dense and dually dense elements are characterized within the Dedekind-completion \((\bar \Omega , \leqslant )\) of (Ω, ≤). As a consequence, A(Ω) has either precisely 5 or at least 22ℵ1 (even maximal) normal subgroups, and various other group- and lattice-theoretic results follow.
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Communicated by A. M. W. Glass
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Droste, M. The normal subgroup lattice of 2-transitive automorphism groups of linearly ordered sets. Order 2, 291–319 (1985). https://doi.org/10.1007/BF00333135
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DOI: https://doi.org/10.1007/BF00333135