{"id":"https://openalex.org/W2039006723","doi":"https://doi.org/10.1142/s021819670500213x","title":"FOLDINGS, GRAPHS OF GROUPS AND THE MEMBERSHIP PROBLEM","display_name":"FOLDINGS, GRAPHS OF GROUPS AND THE MEMBERSHIP PROBLEM","publication_year":2005,"publication_date":"2005-02-01","ids":{"openalex":"https://openalex.org/W2039006723","doi":"https://doi.org/10.1142/s021819670500213x","mag":"2039006723"},"language":"en","primary_location":{"id":"doi:10.1142/s021819670500213x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819670500213x","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/A5023281472","display_name":"Ilya Kapovich","orcid":"https://orcid.org/0000-0002-7694-6236"},"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":"ILYA KAPOVICH","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"],"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":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035673859","display_name":"Richard Weidmann","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"RICHARD WEIDMANN","raw_affiliation_strings":["Fachbereich Mathematik, Johann Wolfgang Goethe-Universit\u00e4t, Robert Mayer-Strasse 6-8, 60325 Frankfurt (Main), Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Johann Wolfgang Goethe-Universit\u00e4t, Robert Mayer-Strasse 6-8, 60325 Frankfurt (Main), Germany","institution_ids":["https://openalex.org/I114090438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112447861","display_name":"Alexei Myasnikov","orcid":null},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ALEXEI MYASNIKOV","raw_affiliation_strings":["Department of Mathematics, City College of CUNY, New York, NY 10031, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City College of CUNY, New York, NY 10031, USA","institution_ids":["https://openalex.org/I125687163"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023281472"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":7.9924,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.98287449,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"01","first_page":"95","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T11567","display_name":"semigroups and automata theory","score":0.9983999729156494,"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":0.9099205732345581},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5562500953674316},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3567834198474884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9099205732345581},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5562500953674316},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3567834198474884}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s021819670500213x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819670500213x","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:CiteSeerX.psu:10.1.1.239.1833","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.1833","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0302206v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.8784","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.8784","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~kapovich/PAPERS/fold.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1234885875","https://openalex.org/W1538946872","https://openalex.org/W1571539704","https://openalex.org/W1578915963","https://openalex.org/W1593585945","https://openalex.org/W1909362234","https://openalex.org/W1963646882","https://openalex.org/W1981155305","https://openalex.org/W1986883817","https://openalex.org/W2009888001","https://openalex.org/W2013461168","https://openalex.org/W2022598306","https://openalex.org/W2025142570","https://openalex.org/W2040960421","https://openalex.org/W2047251067","https://openalex.org/W2058883473","https://openalex.org/W2067839383","https://openalex.org/W2075457192","https://openalex.org/W2083803872","https://openalex.org/W2090588662","https://openalex.org/W2121009792","https://openalex.org/W2130222180","https://openalex.org/W2153126460","https://openalex.org/W2153632678","https://openalex.org/W2266292813","https://openalex.org/W2318910871","https://openalex.org/W2491991712","https://openalex.org/W2492454813","https://openalex.org/W2546671935","https://openalex.org/W2889336407","https://openalex.org/W2991458296","https://openalex.org/W3037845555","https://openalex.org/W3141776272","https://openalex.org/W4230322061","https://openalex.org/W4253313367","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"We":[0,9],"introduce":[1],"a":[2],"combinatorial":[3],"version":[4],"of":[5,20,29,31],"Stallings\u2013Bestvina\u2013Feighn\u2013Dunwoody":[6],"folding":[7],"sequences.":[8],"then":[10],"show":[11],"how":[12],"they":[13],"are":[14],"useful":[15],"in":[16],"analyzing":[17],"the":[18,21],"solvability":[19],"uniform":[22],"subgroup":[23],"membership":[24],"problem":[25],"for":[26],"fundamental":[27],"groups":[28,38],"graphs":[30],"groups.":[32,42],"Applications":[33],"include":[34],"coherent":[35,40],"right-angled":[36],"Artin":[37],"and":[39],"solvable":[41]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}