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Imprimitive permutations in primitive groups
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dc.contributor.author | Araújo, Joao | |
dc.contributor.author | Araújo, Joao Pedro | |
dc.contributor.author | Cameron, Peter Jephson | |
dc.contributor.author | Dobson, Ted | |
dc.contributor.author | Hulpke, Alexander | |
dc.contributor.author | Lopes, Pedro | |
dc.date.accessioned | 2018-05-02T23:33:02Z | |
dc.date.available | 2018-05-02T23:33:02Z | |
dc.date.issued | 2017-09-15 | |
dc.identifier.citation | Araújo , J , Araújo , J P , Cameron , P J , Dobson , T , Hulpke , A & Lopes , P 2017 , ' Imprimitive permutations in primitive groups ' , Journal of Algebra , vol. 486 , pp. 396-416 . https://doi.org/10.1016/j.jalgebra.2017.03.043 | en |
dc.identifier.issn | 0021-8693 | |
dc.identifier.other | PURE: 249397171 | |
dc.identifier.other | PURE UUID: b10d4b89-5e49-4062-bf3b-30fe2c157a3f | |
dc.identifier.other | Scopus: 85020237371 | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/58055570 | |
dc.identifier.other | WOS: 000405447100014 | |
dc.identifier.uri | https://hdl.handle.net/10023/13282 | |
dc.description.abstract | The goal of this paper is to study primitive groups that are contained in the union of maximal (in the symmetric group) imprimitive groups. The study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups. However, this is another instance of a situation common in mathematics in which a very natural problem turns out to be extremely difficult. Fortunately, the enormous progresses of the last few decades seem to allow a new momentum on the attack to this problem. In this paper we prove that there are infinite families of primitive groups contained in the union of imprimitive groups and propose a new hierarchy for primitive groups based on that fact. In addition we introduce some algorithms to handle permutations, provide the corresponding GAP implementation, solve some open problems, and propose a large list of open problems. | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | en |
dc.rights | © 2017, Elsevier, Inc. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://doi.org/10.1016/j.jalgebra.2017.03.043 | en |
dc.subject | Primitive groups | en |
dc.subject | Imprimitive groups | en |
dc.subject | GAP | en |
dc.subject | Permutation type | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Imprimitive permutations in primitive groups | en |
dc.type | Journal article | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1016/j.jalgebra.2017.03.043 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2018-05-02 |
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