Permutation groups without irreducible elements

Glass, AMW and Macpherson, HD orcid.org/0000-0003-0277-7561 (2017) Permutation groups without irreducible elements. In: Droste, M, Fuchs, L, Goldsmith, B and Strüngmann, L, (eds.) Groups, Modules, and Model Theory - Surveys and Recent Developments: In Memory of Rüdiger Göbel. New Pathways between Group Theory and Model Theory, 01-04 Feb 2016, Mülheim an der Ruhr, Germany. Springer , pp. 331-332. ISBN 978-3-319-51717-9

Abstract

We call a non-identity element of a permutation group irreducible if it cannot be written as a product of non-identity elements of disjoint support. We show that it is indeed possible for a sublattice subgroup of Aut(R,≤) to have no irreducible elements and still be transitive on the set of pairs α < β in R . This answers a question raised in “The first-order theory of ℓ-permutation groups”, a Conference talk by the first author.

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Authors/Creators:	Glass, AMW Macpherson, HD https://orcid.org/0000-0003-0277-7561
Copyright, Publisher and Additional Information:	© 2017, Springer International Publishing AG. This is an author produced version of a conference paper published in Groups, Modules, and Model Theory - Surveys and Recent Developments. Uploaded in accordance with the publisher's self-archiving policy.
Keywords:	Order-preserving permutation; ℓ-permutation group
Dates:	Accepted: 9 May 2016 Published (online): 4 June 2019 Published: 4 June 2017
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	12 Aug 2016 11:06
Last Modified:	11 Jul 2019 21:11
Status:	Published
Publisher:	Springer
Identification Number:	https://doi.org/10.1007/978-3-319-51718-6_17

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Permutation groups without irreducible elements

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