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Relations Related to Betweenness: Their Structure and Automorphisms
S. A. Adeleke, Western Illinois University, Macomb, IL, and Peter M. Neumann, Queen's College, Oxford University, England

Memoirs of the American Mathematical Society
1998; 125 pp; softcover
Volume: 131
ISBN-10: 0-8218-0623-8
ISBN-13: 978-0-8218-0623-4
List Price: US$52
Individual Members: US$31.20
Institutional Members: US$41.60
Order Code: MEMO/131/623
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This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, \(C\)-relations and \(D\)-relations. It contains a systematic study of betweenness and introduces \(C\)- and \(D\)-relations to describe the behavior of points at infinity ("leaves" or "ends" or "directions") of trees. The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups.


  • offers the first systematic treatment of betweenness relations
  • introduces important new concepts of \(C\)-relations and \(D\)-relations
  • elucidates the close relationships between semilinear orderings, betweenness relations, \(C\)- and \(D\)-relations
  • considers their automorphism groups as important examples of Jordan permutation groups


Graduate students and research mathematicians interested in relational systems and laws of composition.

Table of Contents

  • Preparation
  • Semilinear order relations
  • Abstract chain sets
  • General betweenness relations
  • Abstract direction sets
  • Applications and commentary
  • References
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