A Transversal Property for Permutation Groups Motivated by Partial Transformations
Group Theory
2019-11-07 v1
Abstract
In this paper we introduce the definition of -universal transversal property, which is a refinement of the definition of -universal transversal property, which in turn is a refinement of the classic definition of -homogeneity for permutation groups. In particular, a group possesses the -universal transversal property if and only if it is primitive; it possesses the -universal transversal property if and only if it is -homogeneous. Up to a few undecided cases, we give a classification of groups satisfying the -universal transversal property, for . Then we apply this result for studying regular semigroups of partial transformations.
Cite
@article{arxiv.1911.02058,
title = {A Transversal Property for Permutation Groups Motivated by Partial Transformations},
author = {João Araújo and João Pedro Araújo and Wolfram Bentz and Peter Cameron and Pablo Spiga},
journal= {arXiv preprint arXiv:1911.02058},
year = {2019}
}