## 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 language | English |
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Pages (from-to) | 741-759 |

Number of pages | 19 |

Journal | Journal of Algebra |

Volume | 573 |

DOIs | |

Publication status | Published - 1 May 2021 |

## Keywords

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