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dc.contributor.authorAraújo, Joao
dc.contributor.authorAraújo, Joao Pedro
dc.contributor.authorCameron, Peter Jephson
dc.contributor.authorDobson, Ted
dc.contributor.authorHulpke, Alexander
dc.contributor.authorLopes, Pedro
dc.identifier.citationAraújo , 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 .
dc.identifier.otherORCID: /0000-0003-3130-9505/work/58055570
dc.description.abstractThe 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.relation.ispartofJournal of Algebraen
dc.subjectPrimitive groupsen
dc.subjectImprimitive groupsen
dc.subjectPermutation typeen
dc.subjectQA Mathematicsen
dc.titleImprimitive permutations in primitive groupsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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