The normal subgroup lattice of 2-transitive automorphism groups of linearly ordered sets |
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Authors: | Manfred Droste |
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Institution: | (1) Fachbereich 6 — Mathematik, Universität GHS Essen, 4300 Essen 1, West-Germany |
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Abstract: | Using combinatorial and model-theoretic means, we examine the structure of normal subgroup lattices N(A( )) of 2-transitive automorphism groups A( ) of infinite linearly ordered sets ( , ). Certain natural sublattices of N(A( )) 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 ( , ). As a consequence, A( ) has either precisely 5 or at least 22 1 (even maximal) normal subgroups, and various other group- and lattice-theoretic results follow. |
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Keywords: | Primary 06F15 Secondary: 20B27 06D15 03C20 |
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