{"id":"https://openalex.org/W2049952790","doi":"https://doi.org/10.1142/s0218196708004883","title":"A QUASI-ISOMETRY INVARIANT LOOP SHORTENING PROPERTY FOR GROUPS","display_name":"A QUASI-ISOMETRY INVARIANT LOOP SHORTENING PROPERTY FOR GROUPS","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2049952790","doi":"https://doi.org/10.1142/s0218196708004883","mag":"2049952790"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004883","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004883","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5080779813","display_name":"Stephen G. Brick","orcid":null},"institutions":[{"id":"https://openalex.org/I83809506","display_name":"University of South Alabama","ror":"https://ror.org/01s7b5y08","country_code":"US","type":"education","lineage":["https://openalex.org/I83809506"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"STEPHEN G. BRICK","raw_affiliation_strings":["Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA","institution_ids":["https://openalex.org/I83809506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051797541","display_name":"Jon M. Corson","orcid":null},"institutions":[{"id":"https://openalex.org/I17301866","display_name":"University of Alabama","ror":"https://ror.org/03xrrjk67","country_code":"US","type":"education","lineage":["https://openalex.org/I17301866"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JON M. CORSON","raw_affiliation_strings":["Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA","Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487 0350, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA","institution_ids":["https://openalex.org/I17301866"]},{"raw_affiliation_string":"Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487 0350, USA","institution_ids":["https://openalex.org/I17301866"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034381429","display_name":"Dohyoung Ryang","orcid":null},"institutions":[{"id":"https://openalex.org/I44854399","display_name":"University of Southern Mississippi","ror":"https://ror.org/0270vfa57","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I44854399"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DOHYOUNG RYANG","raw_affiliation_strings":["Department of Mathematics, University of Southern Mississippi, Long Beach, MS 39560, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Southern Mississippi, Long Beach, MS 39560, USA","institution_ids":["https://openalex.org/I44854399"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080779813"],"corresponding_institution_ids":["https://openalex.org/I83809506"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.1219534,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"18","issue":"08","first_page":"1243","last_page":"1257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9994999766349792,"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/T10849","display_name":"Finite Group Theory Research","score":0.9860000014305115,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9002842903137207},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"Isoperimetric inequality","score":0.8352921009063721},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.5914433002471924},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5889461636543274},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.535617470741272},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5312941670417786},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.4988553524017334},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.48680993914604187},{"id":"https://openalex.org/keywords/finitely-generated-group","display_name":"Finitely generated group","score":0.43258556723594666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3666309714317322},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3485032916069031},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.061223387718200684}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9002842903137207},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.8352921009063721},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.5914433002471924},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5889461636543274},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.535617470741272},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5312941670417786},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.4988553524017334},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.48680993914604187},{"id":"https://openalex.org/C2780811992","wikidata":"https://www.wikidata.org/wiki/Q21083858","display_name":"Finitely generated group","level":3,"score":0.43258556723594666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3666309714317322},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3485032916069031},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061223387718200684},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196708004883","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004883","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:aquila.usm.edu:fac_pubs-2518","is_oa":false,"landing_page_url":"https://aquila.usm.edu/fac_pubs/1519","pdf_url":null,"source":{"id":"https://openalex.org/S4306402529","display_name":"Aquila Digital Community (University of Southern Mississippi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I44854399","host_organization_name":"University of Southern Mississippi","host_organization_lineage":["https://openalex.org/I44854399"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","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":8,"referenced_works":["https://openalex.org/W1545078593","https://openalex.org/W1974276001","https://openalex.org/W2014915809","https://openalex.org/W2045449896","https://openalex.org/W2094731111","https://openalex.org/W2134086356","https://openalex.org/W3104860897","https://openalex.org/W4292101339"],"related_works":["https://openalex.org/W2026092010","https://openalex.org/W1527679771","https://openalex.org/W2963670976","https://openalex.org/W2076039613","https://openalex.org/W4386302958","https://openalex.org/W2771827938","https://openalex.org/W1590360997","https://openalex.org/W2592636924","https://openalex.org/W4368755731","https://openalex.org/W3103704600"],"abstract_inverted_index":{"We":[0],"first":[1],"introduce":[2],"a":[3,31,54,77],"loop":[4,34,68,91],"shortening":[5,35,69,92],"property":[6,12,36,51,70],"for":[7,37],"metric":[8,27],"spaces,":[9],"generalizing":[10],"the":[11,58],"considered":[13],"by":[14],"M.":[15],"Elder":[16],"on":[17],"Cayley":[18],"graphs":[19],"of":[20,57],"finitely":[21,38,62,73],"generated":[22,39,63],"groups.":[23,40],"Then":[24],"using":[25],"this":[26,66,89],"property,":[28],"we":[29],"define":[30],"very":[32],"broad":[33],"Our":[41],"definition":[42],"includes":[43],"Elder's":[44],"groups,":[45],"and":[46,75],"unlike":[47],"his":[48],"definition,":[49],"our":[50],"is":[52,85],"obviously":[53],"quasi-isometry":[55],"invariant":[56],"group.":[59],"Furthermore,":[60],"all":[61],"groups":[64],"satisfying":[65],"general":[67,90],"are":[71],"also":[72],"presented":[74],"satisfy":[76],"quadratic":[78],"isoperimetric":[79],"inequality.":[80],"Every":[81],"CAT(0)":[82],"cubical":[83],"group":[84],"shown":[86],"to":[87],"have":[88],"property.":[93]},"counts_by_year":[{"year":2012,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}