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A transversal property for permutation groups motivated by partial transformations

Research output: Contribution to journalArticlepeer-review

Open Access Status

  • Embargoed (until 5/01/22)

Author(s)

João Araújo, João Pedro Araújo, Wolfram Bentz, Peter J. Cameron, Pablo Spiga

School/Research organisations

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.
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Details

Original languageEnglish
Number of pages19
JournalJournal of Algebra
Early online date5 Jan 2021
DOIs
Publication statusE-pub ahead of print - 5 Jan 2021

    Research areas

  • Primitive permutation groups

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