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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 5, Pages 931–947 (Mi izv1592)  

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

Normal subgroups of free periodic groups

S. I. Adian


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.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:2, 215–229

Bibliographic databases:

Document Type: Article
UDC: 519.4
MSC: Primary 20E05, 20F50; Secondary 20F10
Received: 28.05.1981

Citation: S. I. Adian, “Normal subgroups of free periodic groups”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981), 931–947; Math. USSR-Izv., 19:2 (1982), 215–229

Citation in format AMSBIB
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\by S.~I.~Adian
\paper Normal subgroups of free periodic groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 5
\pages 931--947
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=637610}
\zmath{https://zbmath.org/?q=an:0497.20029}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 215--229
\crossref{https://doi.org/10.1070/IM1982v019n02ABEH001414}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981QB71300001}


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    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. 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
    2. L. D. Beklemishev, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, M. R. Pentus, A. A. Razborov, A. L. Semenov, V. A. Uspenskii, “Sergei Ivanovich Adian (on his 75th birthday)”, Russian Math. Surveys, 61:3 (2006), 575–588  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. S. Atabekyan, “On Periodic Groups of Odd Period $n\ge1003$”, Math. Notes, 82:4 (2007), 443–447  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. S. Atabekyan, “The normalizers of free subgroups in free Burnside groups of odd period $n\ge1003$”, J. Math. Sci., 166:6 (2010), 691–703  mathnet  crossref  mathscinet  elib
    5. S. I. Adian, “The Burnside problem and related topics”, Russian Math. Surveys, 65:5 (2010), 805–855  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. S. Pahlevanyan, “Independent pairs in free Burnside groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 2, 58–62  mathnet
    7. V. S. Atabekyan, “Normal automorphisms of free Burnside groups”, Izv. Math., 75:2 (2011), 223–237  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24  mathnet  crossref  mathscinet  isi
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