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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Abstract(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.

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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

Citation

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.