RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 4, Pages 909–921 (Mi izv1740)  

This article is cited in 3 scientific papers (total in 3 papers)

Some relations between the word and divisibility problems in groups and semigroups

O. A. Sarkisyan


Abstract: This paper studies the relationship between the word problems in a finitely presented semigroup $\Pi$, which is embeddable in a group, and in the group $\Gamma$ with the same generators and defining relations. We construct an example showing that even in the case when not only the word problem but also the left and right divisibility problems are solvable in $\Pi$, the word problem in $\Gamma$ may be unsolvable. Furthermore, we prove that the additional condition of the absence of cycles in the system of defining relations of $\Pi$ issufficient for the solvability of its word and divisibility problems to imply the solvability of the word problem in $\Gamma$.
Bibliography: 3 titles.

Full text: PDF file (1272 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1980, 15:1, 161–171

Bibliographic databases:

UDC: 519.4
MSC: 20F10, 20M05
Received: 20.11.1978

Citation: O. A. Sarkisyan, “Some relations between the word and divisibility problems in groups and semigroups”, Izv. Akad. Nauk SSSR Ser. Mat., 43:4 (1979), 909–921; Math. USSR-Izv., 15:1 (1980), 161–171

Citation in format AMSBIB
\Bibitem{Sar79}
\by O.~A.~Sarkisyan
\paper Some relations between the word and divisibility problems in groups and semigroups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 4
\pages 909--921
\mathnet{http://mi.mathnet.ru/izv1740}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=548509}
\zmath{https://zbmath.org/?q=an:0446.20035|0412.20051}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1980IzMat..15..161S}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 1
\pages 161--171
\crossref{https://doi.org/10.1070/IM1980v015n01ABEH001193}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LB83500007}


Linking options:
  • http://mi.mathnet.ru/eng/izv1740
  • http://mi.mathnet.ru/eng/izv/v43/i4/p909

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. A. Sarkisyan, “On the word and divisibility problems in semigroups and groups without cycles”, Math. USSR-Izv., 19:3 (1982), 643–656  mathnet  crossref  mathscinet  zmath
    2. V. S. Guba, “On the relationship between the problems of equality and divisibility of words for semigroups with a single defining relation”, Izv. Math., 61:6 (1997), 1137–1169  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:269
    Full text:87
    References:36
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020