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A transversal property for permutation groups motivated by partial transformations

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Date
01/05/2021
Author
Araújo, João
Araújo, João Pedro
Bentz, Wolfram
Cameron, Peter J.
Spiga, Pablo
Keywords
Primitive permutation groups
QA Mathematics
Mathematics(all)
T-NDAS
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Abstract
In this paper we introduce the definition of the (k,l)-universal transversal property for permutation groups, which is a refinement of the definition of k-universal transversal property, which in turn is a refinement of the classical definition of k-homogeneity for permutation groups. In particular, a group possesses the (2,n)-universal transversal property if and only if it is primitive; it possesses the (2,2)-universal transversal property if and only if it is 2-homogeneous. Up to a few undecided cases, we give a classification of groups satisfying the (k,l)-universal transversal property, for k ≥ 3. Then we apply this result for studying regular semigroups of partial transformations.
Citation
Araújo , J , Araújo , J P , Bentz , W , Cameron , P J & Spiga , P 2021 , ' A transversal property for permutation groups motivated by partial transformations ' , Journal of Algebra , vol. 573 , pp. 741-759 . https://doi.org/10.1016/j.jalgebra.2020.12.024
Publication
Journal of Algebra
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.jalgebra.2020.12.024
ISSN
0021-8693
Type
Journal article
Rights
Copyright © 2021 Elsevier Inc. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jalgebra.2020.12.024.
Description
Funding: The first and third authors were partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through projects UIDB/00297/2020 Center for Mathematics and Applications) and CEMAT-CIÊNCIAS UID/Multi/04621/2013, and also by the Fundação para a Ciência e a Tecnologia through project PTDC/MAT-PUR/31174/2017. The second author was partially supported by Fundação Calouste Gulbenkian, Programa Talentos Inteligência Artificial. The fourth author was partially supported by Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through project CEMAT-CIÊNCIAS UID/Multi/04621/2013.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/24595

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