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.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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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: |
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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: | 10.1007/978-3-319-51718-6_17 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:102903 |