A transversal property for permutation groups motivated by partial transformations
MetadataShow full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
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.
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
Journal of Algebra
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.
DescriptionFunding: 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.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.