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Abstract
We investigate the structure of the monoid of endomorphisms of the ordered set (Q,≤) of rational numbers. We show that for any countable linearly ordered set Ω, there are uncountably many maximal subgroups of End(Q,≤) isomorphic to the automorphism group of Ω. We characterize those subsets X of Q that arise as a retract in (Q,≤) in terms of topological information concerning X. Finally, we establish that a countable group arises as the automorphism group of a countable linearly ordered set, and hence as a maximal subgroup of End(Q,≤), if and only if it is free abelian of finite rank.
Original language  English 

Pages (fromto)  171194 
Number of pages  24 
Journal  Quarterly Journal of Mathematics 
Volume  70 
Issue number  1 
Early online date  28 Aug 2018 
DOIs  
Publication status  Published  Mar 2019 
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Dive into the research topics of 'Automorphism groups of linearly ordered structures and endomorphisms of the ordered set (Q,≤) of rational numbers'. Together they form a unique fingerprint.Projects
 1 Finished

Automata Languages Decidability: Automata, Languages, Decidability in Algebra
1/03/10 → 31/05/14
Project: Standard
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Martyn Quick
Person: Academic