| Title: | Minimal normal subgroups of transitive permutation groups of square-free degree |
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| Authors: | ID Dobson, Edward (Author)
ID Malnič, Aleksander (Author)
ID Marušič, Dragan (Author)
ID Nowitz, Lewis A. (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.disc.2005.09.029
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | It is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs,Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the fifteenth British combinatorial conference, Discrete Math. 167/168 (1997) 605-615]). |
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| Keywords: | mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph |
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| Year of publishing: | 2007 |
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| Number of pages: | str. 373-385 |
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| Numbering: | Vol. 307, iss. 3-5 |
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| PID: | 20.500.12556/RUP-7719  |
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| ISSN: | 0012-365X |
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| UDC: | 519.17:512.54 |
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| COBISS.SI-ID: | 14179673 |
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| Publication date in RUP: | 02.04.2017 |
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| Views: | 2739 |
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| Downloads: | 93 |
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| Metadata: |    |
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