{"id":"https://openalex.org/W1983860602","doi":"https://doi.org/10.1080/10586458.2003.10504708","title":"On Minimal Length Factorizations of Finite Groups","display_name":"On Minimal Length Factorizations of Finite Groups","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1983860602","doi":"https://doi.org/10.1080/10586458.2003.10504708","mag":"1983860602"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2003.10504708","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2003.10504708","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078462314","display_name":"Mar\u00eda Isabel Gonz\u00e1lez Vasco","orcid":"https://orcid.org/0000-0002-7452-9121"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Mar\u00eda Isabel Gonz\u00e1lez Vasco","raw_affiliation_strings":["\n Departamento de Matematicas, Universidad de Oviedo, c/Calvo Sotelo, s/n, 33007, Oviedo, Spain E-mail: mvasco@orion.ciencias.uniovi.es","Departamento de Matematicas , Universidad de Oviedo , c/Calvo Sotelo, s/n, 33007 , Oviedo , Spain E-mail: mvasco@orion.ciencias.uniovi.es"],"affiliations":[{"raw_affiliation_string":"\n Departamento de Matematicas, Universidad de Oviedo, c/Calvo Sotelo, s/n, 33007, Oviedo, Spain E-mail: mvasco@orion.ciencias.uniovi.es","institution_ids":["https://openalex.org/I165339363"]},{"raw_affiliation_string":"Departamento de Matematicas , Universidad de Oviedo , c/Calvo Sotelo, s/n, 33007 , Oviedo , Spain E-mail: mvasco@orion.ciencias.uniovi.es","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109086831","display_name":"Martin R\u00f6tteler","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Martin R\u00f6tteler","raw_affiliation_strings":["\n Centre for Applied Cryptographic Research, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 E-mail: mroetteler@cacr.math.uwaterloo.ca","Centre for Applied Cryptographic Research, Department of Combinatorics and Optimization , University of Waterloo , Waterloo , Ontario , Canada , N2L 3G1 E-mail: mroetteler@cacr.math.uwaterloo.ca"],"affiliations":[{"raw_affiliation_string":"\n Centre for Applied Cryptographic Research, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 E-mail: mroetteler@cacr.math.uwaterloo.ca","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Centre for Applied Cryptographic Research, Department of Combinatorics and Optimization , University of Waterloo , Waterloo , Ontario , Canada , N2L 3G1 E-mail: mroetteler@cacr.math.uwaterloo.ca","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081329027","display_name":"Rainer Steinwandt","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rainer Steinwandt","raw_affiliation_strings":["\n Institut fur Algorithmen und Kognitive Systeme, Arbeitsgruppe Computeralgebra, Prof. Dr. Th. Beth, Universitat Karlsruhe, 76128, Karlsruhe, Germany E-mail: steinwan@ira.uka.de","Institut fur Algorithmen und Kognitive Systeme, Arbeitsgruppe Computeralgebra, Prof. Dr. Th. Beth, Universitat Karlsruhe , 76128 , Karlsruhe , Germany E-mail: steinwan@ira.uka.de"],"affiliations":[{"raw_affiliation_string":"\n Institut fur Algorithmen und Kognitive Systeme, Arbeitsgruppe Computeralgebra, Prof. Dr. Th. Beth, Universitat Karlsruhe, 76128, Karlsruhe, Germany E-mail: steinwan@ira.uka.de","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Institut fur Algorithmen und Kognitive Systeme, Arbeitsgruppe Computeralgebra, Prof. Dr. Th. Beth, Universitat Karlsruhe , 76128 , Karlsruhe , Germany E-mail: steinwan@ira.uka.de","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078462314"],"corresponding_institution_ids":["https://openalex.org/I165339363"],"apc_list":null,"apc_paid":null,"fwci":1.6504,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.78402813,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"1","first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9908000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.807368278503418},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7991944551467896},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.6117752194404602},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5762136578559875},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5431733131408691},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5315304398536682},{"id":"https://openalex.org/keywords/simple-group","display_name":"Simple group","score":0.49831533432006836},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.48463210463523865},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.46548715233802795},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44512060284614563},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.4163641333580017},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39575591683387756},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37692543864250183},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3341791331768036},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1271720826625824},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11305272579193115},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.09540984034538269},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06427261233329773},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04784214496612549},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.047675520181655884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.807368278503418},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7991944551467896},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6117752194404602},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5762136578559875},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5431733131408691},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5315304398536682},{"id":"https://openalex.org/C5383885","wikidata":"https://www.wikidata.org/wiki/Q571124","display_name":"Simple group","level":3,"score":0.49831533432006836},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.48463210463523865},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.46548715233802795},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44512060284614563},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.4163641333580017},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39575591683387756},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37692543864250183},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3341791331768036},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1271720826625824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11305272579193115},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.09540984034538269},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06427261233329773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04784214496612549},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.047675520181655884},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2003.10504708","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2003.10504708","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1064858780","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1064858780","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.7781","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.7781","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cacr.math.uwaterloo.ca/techreports/2003/corr2003-05.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1494492726","https://openalex.org/W1518203466","https://openalex.org/W1554544277","https://openalex.org/W1570047016","https://openalex.org/W1672460247","https://openalex.org/W1969787312","https://openalex.org/W1976677460","https://openalex.org/W1985080165","https://openalex.org/W1987496014","https://openalex.org/W2024199765","https://openalex.org/W2080309018","https://openalex.org/W2087377210","https://openalex.org/W2092229958","https://openalex.org/W2482011721","https://openalex.org/W2503931018","https://openalex.org/W2611298788","https://openalex.org/W2792609417","https://openalex.org/W3028912885","https://openalex.org/W3042934413","https://openalex.org/W4254866411","https://openalex.org/W4301129560","https://openalex.org/W6637080050"],"related_works":["https://openalex.org/W1555245969","https://openalex.org/W2321282558","https://openalex.org/W2299507895","https://openalex.org/W1900540279","https://openalex.org/W2944491272","https://openalex.org/W2577600644","https://openalex.org/W1866724006","https://openalex.org/W4300498183","https://openalex.org/W2012392278","https://openalex.org/W2656095712"],"abstract_inverted_index":{"Logarithmic":[0],"signatures":[1,18,30,58],"are":[2,19],"a":[3,93],"special":[4,21],"type":[5],"of":[6,12,20,27,66,79],"group":[7,101],"factorizations,\\nintroduced":[8],"as":[9],"basic":[10],"components":[11],"certain":[13],"cryptographic":[14],"keys.\\nThus,":[15],"short":[16],"logarithmic":[17,29,57,96],"interest.\\nWe":[22],"deal":[23],"with":[24],"the":[25,51],"question":[26],"finding":[28],"of\\nminimal":[31],"length":[32,95],"in":[33],"finite":[34,100],"groups.":[35,61],"In":[36],"particular,":[37],"such":[38,67],"factorizations\\nexist":[39],"for":[40,59,69,98],"solvable,":[41],"symmetric,":[42],"and":[43],"alternating":[44],"groups.\\n\u00b6":[45],"We":[46],"show":[47],"how":[48],"to":[49,54],"use":[50],"known":[52],"examples":[53],"derive":[55],"minimal\\nlength":[56],"other":[60],"Namely,":[62],"we":[63],"prove\\nthe":[64],"existence":[65],"factorizations":[68],"several":[70],"classical":[71],"groups\\nand---in":[72],"parts":[73],"by":[74],"direct":[75],"computation---for":[76],"all":[77],"groups":[78],"order\\n<175,560":[80],"($=\\\\ord(J_1)$,":[81],"where":[82],"$J_1$":[83],"is":[84],"Janko's":[85],"first":[86],"sporadic":[87],"simple":[88],"group).":[89],"Whether":[90],"there":[91],"exists":[92],"minimal":[94],"signature":[97],"each":[99],"still":[102],"remains":[103],"an":[104],"open":[105],"question.":[106]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}