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A transversal property for permutation groups motivated by partial transformations

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Τίτλος: A transversal property for permutation groups motivated by partial transformations
Συγγραφείς: Araujo J., Araujo J. P., Bentz W., Cameron P. J., Spiga P.
Συνεισφορές: Araujo, J, Bentz, W, Cameron, P, Spiga, P
Στοιχεία εκδότη: Academic Press Inc.
US
Έτος έκδοσης: 2021
Συλλογή: Università degli Studi di Milano-Bicocca: BOA (Bicocca Open Archive)
Θεματικοί όροι: 2-Transitive group, Partial transformation semigroup, Primitive permutation group, Regular semigroup, Transformation semigroup
Περιγραφή: 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.
Τύπος εγγράφου: article in journal/newspaper
Περιγραφή αρχείου: STAMPA
Γλώσσα: English
Relation: info:eu-repo/semantics/altIdentifier/wos/WOS:000617653500029; volume:573; firstpage:741; lastpage:759; numberofpages:19; journal:JOURNAL OF ALGEBRA; https://hdl.handle.net/10281/416058
DOI: 10.1016/j.jalgebra.2020.12.024
Διαθεσιμότητα: https://hdl.handle.net/10281/416058
https://doi.org/10.1016/j.jalgebra.2020.12.024
Rights: info:eu-repo/semantics/openAccess ; license:Creative Commons ; license uri:http://creativecommons.org/licenses/by/4.0/
Αριθμός Καταχώρησης: edsbas.B8ECDAF2
Βάση Δεδομένων: BASE
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  – Url: https://hdl.handle.net/10281/416058#
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  Data: A transversal property for permutation groups motivated by partial transformations
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  Data: <searchLink fieldCode="AR" term="%22Araujo+J%2E%22">Araujo J.</searchLink><br /><searchLink fieldCode="AR" term="%22Araujo+J%2E+P%2E%22">Araujo J. P.</searchLink><br /><searchLink fieldCode="AR" term="%22Bentz+W%2E%22">Bentz W.</searchLink><br /><searchLink fieldCode="AR" term="%22Cameron+P%2E+J%2E%22">Cameron P. J.</searchLink><br /><searchLink fieldCode="AR" term="%22Spiga+P%2E%22">Spiga P.</searchLink>
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  Data: Araujo, J<br />Bentz, W<br />Cameron, P<br />Spiga, P
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  Data: Academic Press Inc.<br />US
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  Data: 2021
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  Data: Università degli Studi di Milano-Bicocca: BOA (Bicocca Open Archive)
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  Data: <searchLink fieldCode="DE" term="%222-Transitive+group%22">2-Transitive group</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+transformation+semigroup%22">Partial transformation semigroup</searchLink><br /><searchLink fieldCode="DE" term="%22Primitive+permutation+group%22">Primitive permutation group</searchLink><br /><searchLink fieldCode="DE" term="%22Regular+semigroup%22">Regular semigroup</searchLink><br /><searchLink fieldCode="DE" term="%22Transformation+semigroup%22">Transformation semigroup</searchLink>
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  Data: 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.
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  Data: info:eu-repo/semantics/altIdentifier/wos/WOS:000617653500029; volume:573; firstpage:741; lastpage:759; numberofpages:19; journal:JOURNAL OF ALGEBRA; https://hdl.handle.net/10281/416058
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  Data: 10.1016/j.jalgebra.2020.12.024
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  Data: https://hdl.handle.net/10281/416058<br />https://doi.org/10.1016/j.jalgebra.2020.12.024
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  Data: info:eu-repo/semantics/openAccess ; license:Creative Commons ; license uri:http://creativecommons.org/licenses/by/4.0/
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