{"id":"https://openalex.org/W2982636329","doi":"https://doi.org/10.1142/s0218196721400038","title":"Hausdorff dimension of the second Grigorchuk group","display_name":"Hausdorff dimension of the second Grigorchuk group","publication_year":2021,"publication_date":"2021-06-18","ids":{"openalex":"https://openalex.org/W2982636329","doi":"https://doi.org/10.1142/s0218196721400038","mag":"2982636329"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196721400038","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721400038","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1910.14518","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061704102","display_name":"Marialaura Noce","orcid":"https://orcid.org/0000-0002-3729-8598"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marialaura Noce","raw_affiliation_strings":["Mathematisches Institut, Georg-August Universit\u00e4t zu G\u00f6ttingen, Bunsenstr. 3-5, G\u00f6ttingen 37073, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Georg-August Universit\u00e4t zu G\u00f6ttingen, Bunsenstr. 3-5, G\u00f6ttingen 37073, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040799296","display_name":"Anitha Thillaisundaram","orcid":"https://orcid.org/0000-0001-8768-2590"},"institutions":[{"id":"https://openalex.org/I51532219","display_name":"University of Lincoln","ror":"https://ror.org/03yeq9x20","country_code":"GB","type":"education","lineage":["https://openalex.org/I51532219"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Anitha Thillaisundaram","raw_affiliation_strings":["School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln LN6 7TS, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln LN6 7TS, UK","institution_ids":["https://openalex.org/I51532219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061704102"],"corresponding_institution_ids":["https://openalex.org/I74656192"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03143169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"06","first_page":"1037","last_page":"1047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9997000098228455,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9993000030517578,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9958000183105469,"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/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.679466187953949},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.6469032168388367},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6072402000427246},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5973377227783203},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5773904323577881},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5626421570777893},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.5236951112747192},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.49231278896331787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3241031765937805},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32391685247421265},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.25240010023117065},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05771800875663757},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05674096941947937}],"concepts":[{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.679466187953949},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.6469032168388367},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6072402000427246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5973377227783203},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5773904323577881},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5626421570777893},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.5236951112747192},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.49231278896331787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3241031765937805},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32391685247421265},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.25240010023117065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05771800875663757},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05674096941947937},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1142/s0218196721400038","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721400038","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:eprints.lincoln.ac.uk:43116","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196275","display_name":"Lincoln Repository (University of Lincoln)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51532219","host_organization_name":"University of Lincoln","host_organization_lineage":["https://openalex.org/I51532219"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1910.14518","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.14518","pdf_url":"https://arxiv.org/pdf/1910.14518","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null},{"id":"mag:2982636329","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1910.14518","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:figshare.com:article/24387418","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Hausdorff_dimension_of_the_second_Grigorchuk_group/24387418","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/136186","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136186","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1910.14518","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1910.14518","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1910.14518","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.14518","pdf_url":"https://arxiv.org/pdf/1910.14518","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3204101191","display_name":null,"funder_award_id":"EP/T005068/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7827054619","display_name":"Hausdorff dimensions of p-adic analytic groups","funder_award_id":"EP/T005068/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1566117369","https://openalex.org/W1591094656","https://openalex.org/W1713530077","https://openalex.org/W1994543570","https://openalex.org/W2009829154","https://openalex.org/W2042740070","https://openalex.org/W2054363504","https://openalex.org/W2094965802","https://openalex.org/W2114619383","https://openalex.org/W2116802568","https://openalex.org/W2125426572","https://openalex.org/W2130475286","https://openalex.org/W2505618331","https://openalex.org/W2912640957","https://openalex.org/W2963192480","https://openalex.org/W2963861724","https://openalex.org/W3096383168","https://openalex.org/W4210972086"],"related_works":["https://openalex.org/W1563827586","https://openalex.org/W2074376311","https://openalex.org/W3119335068","https://openalex.org/W3100401588","https://openalex.org/W359996409","https://openalex.org/W2048857224","https://openalex.org/W1634353486","https://openalex.org/W3014512901","https://openalex.org/W2964352152","https://openalex.org/W3100205404","https://openalex.org/W2073641655","https://openalex.org/W3006384744","https://openalex.org/W2133232202","https://openalex.org/W2111091142","https://openalex.org/W2963063926","https://openalex.org/W578050539","https://openalex.org/W3081734374","https://openalex.org/W3100066592","https://openalex.org/W2962885948","https://openalex.org/W3047613608"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,21,31],"the":[3,7,10,22,39,44],"Hausdorff":[4],"dimension":[5],"of":[6,9,43],"closure":[8],"second":[11,23],"Grigorchuk":[12,24],"group":[13,25,34,42],"is":[14,26],"[Formula:":[15],"see":[16],"text].":[17],"Furthermore,":[18],"we":[19],"establish":[20],"super":[27],"strongly":[28],"fractal":[29],"and":[30],"its":[32,36],"automorphism":[33,41],"equals":[35],"normalizer":[37],"in":[38],"full":[40],"tree.":[45]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
