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Mathematics of the USSR-Izvestiya, 1982, Volume 19, Issue 2, Pages 215–229
DOI: https://doi.org/10.1070/IM1982v019n02ABEH001414
(Mi im1592)
 

This article is cited in 7 scientific papers (total in 8 papers)

Normal subgroups of free periodic groups

S. I. Adian
References:
Abstract: In this paper the concept of metaperiodic word of a given exponent is introduced, and transformations (reversals) of such words are considered. It is proved that in a free periodic group $B(m,n)$ of any odd exponent $n\geqslant665$ with $m\geqslant66$ generators an infinite independent system of complementary relations can be singled out. It follows that in $B(m,n)$ there exist infinite ascending and descending chains of normal subgroups and also a recursively defined factor group of $B(m,n)$ with an unsolvable identity problem.
Bibliography: 4 titles.
Received: 28.05.1981
Bibliographic databases:
Document Type: Article
UDC: 519.4
MSC: Primary 20E05, 20F50; Secondary 20F10
Language: English
Original paper language: Russian
Citation: S. I. Adian, “Normal subgroups of free periodic groups”, Math. USSR-Izv., 19:2 (1982), 215–229
Citation in format AMSBIB
\Bibitem{Adi81}
\by S.~I.~Adian
\paper Normal subgroups of free periodic groups
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 215--229
\mathnet{http://mi.mathnet.ru//eng/im1592}
\crossref{https://doi.org/10.1070/IM1982v019n02ABEH001414}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=637610}
\zmath{https://zbmath.org/?q=an:0497.20029}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981QB71300001}
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  • https://www.mathnet.ru/eng/im1592
  • https://doi.org/10.1070/IM1982v019n02ABEH001414
  • https://www.mathnet.ru/eng/im/v45/i5/p931
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:473
    Russian version PDF:105
    English version PDF:15
    References:47
    First page:3
     
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