A transversal property for permutation groups motivated by partial transformations
Date
01/05/2021Metadata
Show full item recordAbstract
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
ISSN
0021-8693Type
Journal article
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.Collections
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