{"id":"https://openalex.org/W2146358528","doi":"https://doi.org/10.1142/s021819671250021x","title":"NON-RIGIDITY OF CYCLIC AUTOMORPHIC ORBITS IN FREE GROUPS","display_name":"NON-RIGIDITY OF CYCLIC AUTOMORPHIC ORBITS IN FREE GROUPS","publication_year":2011,"publication_date":"2011-11-14","ids":{"openalex":"https://openalex.org/W2146358528","doi":"https://doi.org/10.1142/s021819671250021x","mag":"2146358528"},"language":"en","primary_location":{"id":"doi:10.1142/s021819671250021x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671250021x","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":null,"display_name":"BRIAN RAY","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"BRIAN RAY","raw_affiliation_strings":["Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA","Department of Mathematics, University of Illinois at Urbana - Champaign, 1409 West Green Street, Urbana, IL 61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana - Champaign, 1409 West Green Street, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.5045,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.82676473,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"22","issue":"03","first_page":"1250021","last_page":"1250021"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"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":0.9998000264167786,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9919999837875366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9200489521026611},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6898114681243896},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.6293642520904541},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5655347108840942},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.48771676421165466},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.4494277834892273},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05584460496902466}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9200489521026611},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6898114681243896},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6293642520904541},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5655347108840942},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.48771676421165466},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.4494277834892273},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05584460496902466},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819671250021x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671250021x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W54401119","https://openalex.org/W57410823","https://openalex.org/W644799305","https://openalex.org/W646383846","https://openalex.org/W1493863997","https://openalex.org/W1965550608","https://openalex.org/W1983883140","https://openalex.org/W2014241211","https://openalex.org/W2017555647","https://openalex.org/W2034592120","https://openalex.org/W2076181847","https://openalex.org/W4205309529"],"related_works":["https://openalex.org/W2626846570","https://openalex.org/W2068558458","https://openalex.org/W3204534828","https://openalex.org/W1541799442","https://openalex.org/W2369416114","https://openalex.org/W1974121318","https://openalex.org/W2100019499","https://openalex.org/W2152992791","https://openalex.org/W2067074449","https://openalex.org/W4297837809"],"abstract_inverted_index":{"We":[0],"say":[1],"a":[2],"subset":[3],"\u03a3":[4,113,140],"\u2286":[5],"F":[6,85,92,135],"N":[7,14,27,56,73,86,93,130,136],"of":[8,12,61,64,99,104],"the":[9,138],"free":[10],"group":[11],"rank":[13],"is":[15,74,95,114,146],"spectrally":[16,96,115,148],"rigid":[17],"if":[18],"whenever":[19],"T":[20,23,37,41,49,52,70,83],"1":[21,38,50],",":[22,137],"2":[24,42,53],"\u2208":[25,46,71,127,134],"cv":[26,55,72],"are":[28],"\u211d-trees":[29,67],"in":[30,54],"(unprojectivized)":[31],"outer":[32],"space":[33],"for":[34,43,124],"which":[35],"\u2016\u03c3\u2016":[36,40],"=":[39,51,141],"every":[44],"\u03c3":[45],"\u03a3,":[47],"then":[48],".":[57],"The":[58],"general":[59],"theory":[60],"(non-abelian)":[62],"actions":[63],"groups":[65],"on":[66,118],"establishes":[68],"that":[69,91,110,123],"uniquely":[75],"determined":[76],"by":[77],"its":[78],"translation":[79],"length":[80],"function":[81],"\u2016\u22c5\u2016":[82],":":[84],"\u2192":[87],"\u211d,":[88],"and":[89,101,103,107,132],"consequently":[90],"itself":[94],"rigid.":[97,116,149],"Results":[98],"Smillie":[100],"Vogtmann,":[102],"Cohen,":[105],"Lustig":[106],"Steiner":[108],"establish":[109],"no":[111],"finite":[112],"Capitalizing":[117],"their":[119],"constructions,":[120],"we":[121],"prove":[122],"any":[125],"\u03a6":[126],"Aut":[128],"(F":[129],")":[131],"g":[133],"set":[139],"{\u03a6":[142],"n":[143],"(g)}":[144],"n\u2208\u2124":[145],"not":[147]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}