A transversal property for permutation groups motivated by partial transformations

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)741-759
Number of pages19
JournalJournal of Algebra
Volume573
DOIs
Publication statusPublished - 1 May 2021

Keywords

  • 2-Transitive groups
  • Partial transformation semigroups
  • Primitive permutation groups
  • Regular semigroups
  • Transformation semigroups

Fingerprint

Dive into the research topics of 'A transversal property for permutation groups motivated by partial transformations'. Together they form a unique fingerprint.

Cite this