Normal subgroups of doubly transitive automorphism groups of chains-Reference-Cited by-同舟云学术

Normal subgroups of doubly transitive automorphism groups of chains

Published:1985 Issue:2 Volume:290 Page:647-664
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Ball Richard N.,Droste Manfred

Abstract

We characterize the structure of the normal subgroup lattice of 2 2 -transitive automorphism groups A ( Ω ) A(\Omega ) of infinite chains ( Ω , ⩽ ) (\Omega , \leqslant ) by the structure of the Dedekind completion ( Ω ¯ , ⩽ ) (\bar \Omega , \leqslant ) of the chain ( Ω , ⩽ ) (\Omega , \leqslant ) . As a consequence we obtain various group-theoretical results on the normal subgroups of A ( Ω ) A(\Omega ) , including that any proper subnormal subgroup of A ( Ω ) A(\Omega ) is indeed normal and contained in a maximal proper normal subgroup of A ( Ω ) A(\Omega ) , and that A ( Ω ) A(\Omega ) has precisely 5 5 normal subgroups if and only if the coterminality of the chain ( Ω , ⩽ ) (\Omega , \leqslant ) is countable.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1985-290-02/S0002-9947-1985-0792817-5/S0002-9947-1985-0792817-5.pdf

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