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Automorphism Groups of Homogeneous Semilinear Orders: Normal Subgroups and Commutators

Published online by Cambridge University Press:  20 November 2018

M. Droste ,
W. C. Holland  and
H. D. Macpherson
M. Droste
Affiliation:
Fachbereich 6-Mathematik und Informatik, UniversitätGHS Essen, D-4300 Essen 1, Federal Republic of Germany
W. C. Holland
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, USA
H. D. Macpherson
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, LondonE1 4NS, England
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A partially ordered set (T, ≤) is called a tree if it is semilinearly ordered, i.e. any two elements have a common lower bound but no two incomparable elements have a common upper bound, and contains an infinite chain and at least two incomparable elements. Let k ∈ ℕ. We say that a partially ordered set (T, ≤) is k-homogeneous, if each isomorphism between two k-element subsets of T extends to an automorphism of (T, ≤), and weakly k-transitive, if for any two k-element subchains of T there exists an automorphism of (T, ≤) taking one to the other.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 4 , 01 August 1991 , pp. 721 - 737
Copyright
Copyright © Canadian Mathematical Society 1991

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