A transversal property for permutation groups motivated by partial transformations

Araújo, João; Araújo, João Pedro; Bentz, Wolfram; Cameron, Peter; Spiga, Pablo

http://hdl.handle.net/10400.2/13248

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Resumo(s)

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 refine- ment 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.

Descrição

Preprint de J. Araújo, J.P. Araújo, W. Bentz, P.J. Cameron, and P. Spiga, “A Transversal Property for Permutation Groups Motivated by Partial Transformations”, Journal of Algebra 573 (2021), 741-759.

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http://hdl.handle.net/10400.2/13248

Citação

J. Araújo, J.P. Araújo, W. Bentz, P.J. Cameron, and P. Spiga, “A Transversal Property for Permutation Groups Moti- vated by Partial Transformations”, Journal of Algebra 573 (2021), 741-759.