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Automorphism Groups of Infinite Semilinear Orders (I)
Author(s) -
Droste M.,
Holland W. C.,
Macpherson H. D.
Publication year - 1989
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-58.3.454
Subject(s) - mathematics , automorphism , categorical variable , combinatorics , automorphism group , normal subgroup , outer automorphism group , inner automorphism , partially ordered set , graph automorphism , graph , group (periodic table) , pure mathematics , discrete mathematics , statistics , line graph , voltage graph , chemistry , organic chemistry
Results are obtained concerning normal subgroups of the automorphism groups of certain infinite trees. These structures are mostly ℵ o ‐categorical, and are trees in a poset‐theoretic but not graph‐theoretic sense. It is shown that the automorphism group has a smallest non‐trivial normal subgroup, a largest proper normal subgroup, and at least 2 2ο normal subgroups between these two. We also obtain and use some results on groups of automorphisms of chains.