{"id":"https://openalex.org/W7213600063","doi":"https://doi.org/10.48550/arxiv.2609.20028","title":"Magma Automorphisms and Quasi-Linear Cycle Sets","display_name":"Magma Automorphisms and Quasi-Linear Cycle Sets","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213600063","doi":"https://doi.org/10.48550/arxiv.2609.20028"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20028","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20028","pdf_url":"https://arxiv.org/pdf/2609.20028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.20028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067334578","display_name":"Nigel P. Byott","orcid":"https://orcid.org/0000-0003-4827-0459","observed_orcids":["https://orcid.org/0000-0003-4827-0459"]},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Byott, Nigel P.","raw_affiliation_strings":["Department of Mathematics & Statistics , University of Exeter , Ex- eter EX4 4QF , U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics , University of Exeter , Ex- eter EX4 4QF , U.K","institution_ids":["https://openalex.org/I23923803"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152116239","display_name":"Edgar Jasko","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]},{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE","GB"],"is_corresponding":false,"raw_author_name":"Jasko, Edgar","raw_affiliation_strings":["Department of Mathematics & Statistics , University of Exeter , Ex- eter EX4 4QF , U.K","Department of Mathematics , KU Leuven , B-3001 Leuven , Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics , University of Exeter , Ex- eter EX4 4QF , U.K","institution_ids":["https://openalex.org/I23923803"]},{"raw_affiliation_string":"Department of Mathematics , KU Leuven , B-3001 Leuven , Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.41749998927116394,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.41749998927116394,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.20200000703334808,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.14489999413490295,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonassociative-algebras","display_name":"nonassociative algebras","score":0.4740000069141388},{"id":"https://openalex.org/keywords/conjecture","display_name":"conjecture","score":0.35100001096725464}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.8939999938011169},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7465000152587891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6238999962806702},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5633000135421753},{"id":"https://openalex.org/C183222429","wikidata":"https://www.wikidata.org/wiki/Q42278","display_name":"Magma","level":3,"score":0.5246000289916992},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38589999079704285},{"id":"https://openalex.org/C198800484","wikidata":"https://www.wikidata.org/wiki/Q1503423","display_name":"Quasigroup","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.3741999864578247},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3522000014781952},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30640000104904175},{"id":"https://openalex.org/C162619202","wikidata":"https://www.wikidata.org/wiki/Q4826703","display_name":"Automorphisms of the symmetric and alternating groups","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.298799991607666},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20028","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20028","pdf_url":"https://arxiv.org/pdf/2609.20028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.20028","doi":"https://doi.org/10.48550/arxiv.2609.20028","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20028","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.20028","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20028","pdf_url":"https://arxiv.org/pdf/2609.20028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5714551453","display_name":"Hopf-Galois Theory and Skew Braces","funder_award_id":"EP/V005995/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320184","display_name":"London Mathematical Society","ror":"https://ror.org/01r1e1h27"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213600063.pdf","grobid_xml":"https://content.openalex.org/works/W7213600063.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7024003306","https://openalex.org/W1975775830","https://openalex.org/W6996342227","https://openalex.org/W1688101452","https://openalex.org/W3133456501","https://openalex.org/W2067861135","https://openalex.org/W2955541056","https://openalex.org/W615355750","https://openalex.org/W2995388531","https://openalex.org/W4410293975"],"abstract_inverted_index":{"Rump":[0],"asked":[1],"in":[2,25,52],"2016":[3],"whether":[4],"every":[5],"finite":[6],"quasi-linear":[7],"cycle":[8],"set":[9],"is":[10],"retractible.":[11],"This":[12],"was":[13],"recently":[14],"proved":[15],"by":[16],"Dietzel.":[17],"In":[18],"this":[19],"paper,":[20],"we":[21],"reinterpret":[22],"Rump's":[23],"question":[24],"terms":[26],"of":[27,29,42,54],"automorphisms":[28,41],"certain":[30],"pointed":[31],"magmas,":[32],"and":[33,49],"propose":[34],"a":[35],"more":[36],"general":[37],"conjecture":[38],"on":[39],"the":[40],"these":[43],"magmas.":[44],"We":[45],"provide":[46],"some":[47],"theoretical":[48],"computational":[50],"evidence":[51],"support":[53],"our":[55],"conjecture.":[56]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-19T00:00:00"}
