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Pre-primitive permutation groups
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dc.contributor.author | Anagnostopoulou-Merkouri, Marina | |
dc.contributor.author | Cameron, Peter J. | |
dc.contributor.author | Suleiman, Enoch | |
dc.date.accessioned | 2023-09-25T14:30:05Z | |
dc.date.available | 2023-09-25T14:30:05Z | |
dc.date.issued | 2023-12-15 | |
dc.identifier | 293802862 | |
dc.identifier | b5e63aa3-59dd-463e-be85-b76b38f457f4 | |
dc.identifier | 85171685967 | |
dc.identifier.citation | Anagnostopoulou-Merkouri , M , Cameron , P J & Suleiman , E 2023 , ' Pre-primitive permutation groups ' , Journal of Algebra , vol. 636 , pp. 695-715 . https://doi.org/10.1016/j.jalgebra.2023.09.012 | en |
dc.identifier.issn | 0021-8693 | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/142904501 | |
dc.identifier.uri | https://hdl.handle.net/10023/28446 | |
dc.description | Funding: The first author was funded by a StARIS research internship from the University of St Andrews. | en |
dc.description.abstract | A transitive permutation group G on a finite set Omega is said to be pre-primitive if every G-invariant partition of Omega is the orbit partition of a subgroup of G. It follows that pre-primitivity and quasiprimitivity are logically independent (there are groups satisfying one but not the other) and their conjunction is equivalent to primitivity. Indeed, part of the motivation for studying pre-primitivity is to investigate the gap between primitivity and quasiprimitivity. We investigate the pre-primitivity of various classes of transitive groups including groups with regular normal subgroups, direct and wreath products, and diagonal groups. In the course of this investigation, we describe all G-invariant partitions for various classes of permutation groups G. We also look briefly at conditions similarly related to other pairs of conditions, including transitivity and quasiprimitivity, k-homogeneity and k-transitivity, and primitivity and synchronization. | |
dc.format.extent | 418992 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | en |
dc.subject | Transitive permutation group | en |
dc.subject | Invariant partition | en |
dc.subject | Quasiprimitivity | en |
dc.subject | QA Mathematics | en |
dc.subject | Mathematics(all) | en |
dc.subject | T-DAS | en |
dc.subject.lcc | QA | en |
dc.title | Pre-primitive permutation groups | en |
dc.type | Journal article | 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.2023.09.012 | |
dc.description.status | Peer reviewed | en |
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