A construction of all normal subgroup lattices of 2-transitive automorphism groups of linearly ordered sets

Manfred Droste; Saharon Shelah

doi:10.1007/BF02772666

A construction of all normal subgroup lattices of 2-transitive automorphism groups of linearly ordered sets

Manfred Droste^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We give a complete classification and construction of all normal subgroup lattices of 2-transitive automorphism groups A(Ω) of linearly ordered sets (Ω, ≦). We also show that in each of these normal subgroup lattices, the partially ordered subset of all those elements which are finitely generated as normal subgroups forms a lattice which is closed under even countably-infinite intersections, and we derive several further group-theoretical consequences from our classification.

Original language	English
Pages (from-to)	223-261
Number of pages	39
Journal	Israel Journal of Mathematics
Volume	51
Issue number	3
DOIs	https://doi.org/10.1007/BF02772666
State	Published - Sep 1985

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abstract = "We give a complete classification and construction of all normal subgroup lattices of 2-transitive automorphism groups A(Ω) of linearly ordered sets (Ω, ≦). We also show that in each of these normal subgroup lattices, the partially ordered subset of all those elements which are finitely generated as normal subgroups forms a lattice which is closed under even countably-infinite intersections, and we derive several further group-theoretical consequences from our classification.",

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AB - We give a complete classification and construction of all normal subgroup lattices of 2-transitive automorphism groups A(Ω) of linearly ordered sets (Ω, ≦). We also show that in each of these normal subgroup lattices, the partially ordered subset of all those elements which are finitely generated as normal subgroups forms a lattice which is closed under even countably-infinite intersections, and we derive several further group-theoretical consequences from our classification.

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A construction of all normal subgroup lattices of 2-transitive automorphism groups of linearly ordered sets

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