Algorithmic theory of solvable groups

The purpose of this survey is to give some picture of what is known about algorithmic and decision problems in the theory of solvable groups. We will provide a number of references to various results, which are presented without proof. Naturally, the choice of the material reported on reflects the a...

Full description

Saved in:
Bibliographic Details
Published in:Prikladnaya Diskretnaya Matematika no. 52; pp. 16 - 64
Main Author: Roman’kov, V. A.
Format: Journal Article
Language:English
Published: 2021
ISSN:2071-0410, 2311-2263
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The purpose of this survey is to give some picture of what is known about algorithmic and decision problems in the theory of solvable groups. We will provide a number of references to various results, which are presented without proof. Naturally, the choice of the material reported on reflects the author’s interests and many worthy contributions to the field will unfortunately go without mentioning. In addition to achievements in solving classical algorithmic problems, the survey presents results on other issues. Attention is paid to various aspects of modern theory related to the complexity of algorithms, their practical implementation, random choice, asymptotic properties. Results are given on various issues related to mathematical logic and model theory. In particular, a special section of the survey is devoted to elementary and universal theories of solvable groups. Special attention is paid to algorithmic questions regarding rational subsets of groups. Results on algorithmic problems related to homomorphisms, automorphisms, and endomorphisms of groups are presented in sufficient detail.
AbstractList The purpose of this survey is to give some picture of what is known about algorithmic and decision problems in the theory of solvable groups. We will provide a number of references to various results, which are presented without proof. Naturally, the choice of the material reported on reflects the author’s interests and many worthy contributions to the field will unfortunately go without mentioning. In addition to achievements in solving classical algorithmic problems, the survey presents results on other issues. Attention is paid to various aspects of modern theory related to the complexity of algorithms, their practical implementation, random choice, asymptotic properties. Results are given on various issues related to mathematical logic and model theory. In particular, a special section of the survey is devoted to elementary and universal theories of solvable groups. Special attention is paid to algorithmic questions regarding rational subsets of groups. Results on algorithmic problems related to homomorphisms, automorphisms, and endomorphisms of groups are presented in sufficient detail.
Author Roman’kov, V. A.
Author_xml – sequence: 1
  givenname: V. A.
  surname: Roman’kov
  fullname: Roman’kov, V. A.
BookMark eNp1j0tLw0AUhQepYK3dus7GZZo7dx5JlqWoFQpudB0mkzvtQJopM1Hovze-NoKrc-DwHfiu2WwIAzF2y2HFS0RRIJQcJIdCYYEXbI6C8xxRi9nUpy3_HK_YMiXfAsgSpMZ6zu7W_T5EPx6O3mbjgUI8Z8FlKfTvpu0p28fwdko37NKZPtHyJxfs9eH-ZbPNd8-PT5v1Lrco6jE3opLQgVDAubBoeA2qIw3UttJxV1GlHaEjbUUniUoypuy0Aus0KN6RWDD5_WtjSCmSa6wfzejDMEbj-4ZD82Xb_No2ChucsNUf7BT90cTzf8AHPrxXBA
CitedBy_id crossref_primary_10_1515_jgth_2023_0119
ContentType Journal Article
CorporateAuthor Dostoevsky Omsk State University
Institute of Mathematics. S. L. Sobolev SB RAS
CorporateAuthor_xml – name: Institute of Mathematics. S. L. Sobolev SB RAS
– name: Dostoevsky Omsk State University
DBID AAYXX
CITATION
DOI 10.17223/20710410/52/2
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
DeliveryMethod fulltext_linktorsrc
EISSN 2311-2263
EndPage 64
ExternalDocumentID 10_17223_20710410_52_2
GroupedDBID AAYXX
AFOEB
ALMA_UNASSIGNED_HOLDINGS
CITATION
VCL
VIT
ID FETCH-LOGICAL-c239t-a3840d0350113c2a1905de60ebb4f1f8e86fe2fe6c3d4ee7eaa7d650cf6051de3
ISICitedReferencesCount 3
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000667023600002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2071-0410
IngestDate Tue Nov 18 22:06:29 EST 2025
Sat Nov 29 02:09:37 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 52
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c239t-a3840d0350113c2a1905de60ebb4f1f8e86fe2fe6c3d4ee7eaa7d650cf6051de3
PageCount 49
ParticipantIDs crossref_citationtrail_10_17223_20710410_52_2
crossref_primary_10_17223_20710410_52_2
PublicationCentury 2000
PublicationDate 2021-00-00
PublicationDateYYYYMMDD 2021-01-01
PublicationDate_xml – year: 2021
  text: 2021-00-00
PublicationDecade 2020
PublicationTitle Prikladnaya Diskretnaya Matematika
PublicationYear 2021
SSID ssib004704629
ssib015894985
ssib057823097
ssib044756707
ssib008678967
Score 2.151876
SecondaryResourceType review_article
Snippet The purpose of this survey is to give some picture of what is known about algorithmic and decision problems in the theory of solvable groups. We will provide a...
SourceID crossref
SourceType Enrichment Source
Index Database
StartPage 16
Title Algorithmic theory of solvable groups
WOSCitedRecordID wos000667023600002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2311-2263
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssib044756707
  issn: 2071-0410
  databaseCode: M~E
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZQ4cAFgQBRHlUOIA7I3fiR2D6uqlY9QFWhIvUWOfYEql0l1e6yKhd-O2M7m4SXVA5cIsuyZrP7bcbfODPfEPLaGPC69oK6xjoqZe6obqCkknnjcl94ZWPXkvfq7ExfXprzvuvaOrYTUG2rb27M9X-FGucQ7FA6-w9wD0ZxAscIOl4RdrzeCvj58nOHEf-XkPQeyxTjO3T8zG2skoplHOspJz1fXS2W1rf2mw1inIsVbOL4g00az4vBc3_swnlpnx5hFt02ZskevpsfTg8PUi1y8i4cuQXNZZ9TCmlOMEaRj4kJ8ElftndvrJxslEl9_DcXrHjUggj2g3kcFnwoO_lJ7_qXfWjIDgxxSbBS7WxUBa9wm73LFYY_IT3z-_Hoc1Qorx0pmcbd14yUihXaSDPq8wR9w1KNIW9Q8xd57MEz_CK9tme4hdnuFmYFn_EJd5mQkIuH5EEfPWTzhPojcgfax-TNBPEsIZ51TbZDPEuIPyGfTo4vjk5p3_2COi7MhlqBsbePL36ZcNwicys8lDnUtWxYo0GXDXB8rpzwEkCBtcoj33YNRqjMg3hK9tquhWckU45DrTzn-ABKaKT12uUgawlCuNKzfUJ336tyvTR86FCyrP4MxT55O6y_TqIof1n5_NYrX5D74Q-aTrdekr3N6iu8IvfcdnO1Xh1EzH8AAo1LbQ
linkProvider ISSN International Centre
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Algorithmic+theory+of+solvable+groups&rft.jtitle=Prikladnaya+Diskretnaya+Matematika&rft.au=Roman%E2%80%99kov%2C+V.+A.&rft.date=2021&rft.issn=2071-0410&rft.eissn=2311-2263&rft.issue=52&rft.spage=16&rft.epage=64&rft_id=info:doi/10.17223%2F20710410%2F52%2F2&rft.externalDBID=n%2Fa&rft.externalDocID=10_17223_20710410_52_2
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2071-0410&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2071-0410&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2071-0410&client=summon