{"id":"https://openalex.org/W4321360458","doi":"https://doi.org/10.3103/s0146411622070203","title":"Computational Analysis of Quantitative Characteristics of Some Residual Properties of Solvable Baumslag\u2013Solitar Groups","display_name":"Computational Analysis of Quantitative Characteristics of Some Residual Properties of Solvable Baumslag\u2013Solitar Groups","publication_year":2022,"publication_date":"2022-12-01","ids":{"openalex":"https://openalex.org/W4321360458","doi":"https://doi.org/10.3103/s0146411622070203"},"language":"en","primary_location":{"id":"doi:10.3103/s0146411622070203","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411622070203","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","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/A5090608830","display_name":"E. A. Tumanova","orcid":"https://orcid.org/0000-0002-6193-9834"},"institutions":[{"id":"https://openalex.org/I120930651","display_name":"Ivanovo State University","ror":"https://ror.org/03rqm8n56","country_code":"RU","type":"education","lineage":["https://openalex.org/I120930651"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"E. A. Tumanova","raw_affiliation_strings":["Ivanovo State University, 153025, Ivanovo, Russia","Ivanovo State University, Ivanovo, Russia"],"raw_orcid":"https://orcid.org/0000-0002-6193-9834","affiliations":[{"raw_affiliation_string":"Ivanovo State University, 153025, Ivanovo, Russia","institution_ids":["https://openalex.org/I120930651"]},{"raw_affiliation_string":"Ivanovo State University, Ivanovo, Russia","institution_ids":["https://openalex.org/I120930651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090608830"],"corresponding_institution_ids":["https://openalex.org/I120930651"],"apc_list":null,"apc_paid":null,"fwci":0.1312,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55643317,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"56","issue":"7","first_page":"800","last_page":"806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11797","display_name":"graph theory and CDMA systems","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9721999764442444,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7449200749397278},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.7381811141967773},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6864194869995117},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5870435833930969},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5718508958816528},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5666221380233765},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5195301175117493},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4686638116836548},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.41602790355682373},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3833346962928772},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13019469380378723},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12469401955604553}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7449200749397278},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7381811141967773},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6864194869995117},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5870435833930969},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5718508958816528},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5666221380233765},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5195301175117493},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4686638116836548},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.41602790355682373},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3833346962928772},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13019469380378723},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12469401955604553},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3103/s0146411622070203","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411622070203","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1973552094","https://openalex.org/W1974781712","https://openalex.org/W2076927847"],"related_works":["https://openalex.org/W2293209037","https://openalex.org/W2901832352","https://openalex.org/W2915925709","https://openalex.org/W2020737723","https://openalex.org/W3098388960","https://openalex.org/W2333358997","https://openalex.org/W2149955913","https://openalex.org/W4300078456","https://openalex.org/W1703119562","https://openalex.org/W2390557090"],"abstract_inverted_index":{"Let":[0],"Gk":[1,5,31,66],"be":[2,122,200],"defined":[3],"as":[4],"=":[6,11,62,75,148],"$$\\left\\langle":[7],"{a,b;{{a}^{{":[8],"-":[9],"1}}}ba":[10],"{{b}^{k}}}":[12],"\\right\\rangle":[13],"$$":[14,136,142],",":[15],"where":[16,208],"k":[17,54,84,137,143,156,195,216,237],"\u2260":[18],"0.":[19],"It":[20,41],"is":[21,26,32,42,67,93,159,212,238,261],"known":[22,44],"that":[23,45,110,130],"if":[24,46,176],"p":[25,47,57,131,134,163],"a":[27,34,69,94,160,246],"prime":[28,108,250],"number":[29,103,124],"then":[30,65,190],"residually":[33,68],"finite":[35,70],"p-group":[36],"iff":[37,72],"p|k":[38],"\u2013":[39,55,78,138,144,151],"1.":[40],"also":[43],"and":[48,60,80,162,164,183,217,240,274],"q":[49,59,140,158,165],"are":[50,166],"primes":[51],"not":[52],"dividing":[53],"1,":[56,76,139,145,149,152],"<":[58,132],"\u03c0":[61],"{p,":[63,127],"q}":[64,128],"\u03c0-group":[71],"(k,":[73,146],"q)":[74,147],"p|q":[77,150],"1":[79,184],"the":[81,86,90,99,102,112,115,123,153,169,196,205,209,229,232,255,258,269],"order":[82,154],"of":[83,89,101,104,107,114,125,155,231,249,257,271],"in":[85,268],"multiplicative":[87],"group":[88],"field":[91],"\u2124q":[92],"p-number.":[95],"This":[96],"paper":[97],"examines":[98],"question":[100],"two-element":[105,247],"sets":[106,126],"numbers":[109,251],"satisfy":[111],"conditions":[113,256],"last":[116,259],"criterion.":[117],"More":[118],"precisely,":[119],"let":[120],"fk(x)":[121,198],"such":[129],"q,":[133],"$$\\nmid":[135,141],"modulo":[157],"p-number,":[161],"chosen":[167],"among":[168],"first":[170],"x":[171,186],"primes.":[172],"We":[173],"state":[174],"that,":[175],"2":[177],"\u2264":[178,180,185,187,219,221],"|k|":[179,220],"10":[181,222],"000":[182],"50":[188],"000,":[189],"for":[191,214,244,252],"almost":[192],"all":[193],"considered":[194],"function":[197,206],"can":[199],"approximated":[201],"quite":[202],"accurately":[203],"by":[204],"\u03b1kx0.85,":[207],"coefficient":[210],"\u03b1k":[211],"different":[213],"each":[215],"{\u03b1k|2":[218],"000}":[223],"\u2286":[224],"(0.28;":[225],"0.31].":[226],"In":[227],"addition,":[228],"dependence":[230],"value":[233],"fk(50":[234],"000)":[235],"on":[236],"investigated":[239],"an":[241],"effective":[242],"algorithm":[243],"checking":[245],"set":[248],"compliance":[253],"with":[254],"criterion":[260],"proposed.":[262],"The":[263],"results":[264],"may":[265],"have":[266],"applications":[267],"theory":[270],"computational":[272],"complexity":[273],"algebraic":[275],"cryptography.":[276]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}