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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 4, Pages 971–979 (Mi izv2500)  

This article is cited in 11 scientific papers (total in 12 papers)

Defining relations and the word problem for free periodic groups of odd order

P. S. Novikov, S. I. Adian

Abstract: We prove that the free periodic group of odd order $n\geqslant4381$ with $m>1$ generators cannot be given by a finite number of defining relations. The word problem for these groups is solvable.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:4, 935–942

Bibliographic databases:

UDC: 519.4
MSC: 20F05, 20F50, 20D10
Received: 19.03.1968

Citation: P. S. Novikov, S. I. Adian, “Defining relations and the word problem for free periodic groups of odd order”, Izv. Akad. Nauk SSSR Ser. Mat., 32:4 (1968), 971–979; Math. USSR-Izv., 2:4 (1968), 935–942

Citation in format AMSBIB
\by P.~S.~Novikov, S.~I.~Adian
\paper Defining relations and the word problem for free periodic groups of odd order
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 4
\pages 971--979
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 4
\pages 935--942

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. S. Novikov, S. I. Adian, “On abelian subgroups and the conjugacy problem in free periodic groups of odd order”, Math. USSR-Izv., 2:5 (1968), 1131–1144  mathnet  crossref  mathscinet  zmath
    2. S. I. Adian, “On some torsion-free groups”, Math. USSR-Izv., 5:3 (1971), 475–484  mathnet  crossref  mathscinet  zmath
    3. V. L. Shirvanyan, “Independent systems of defining relations for a free periodic group of odd exponent”, Math. USSR-Sb., 29:1 (1976), 119–122  mathnet  crossref  mathscinet  zmath  isi
    4. S. I. Adian, “An axiomatic method of constructing groups with given properties”, Russian Math. Surveys, 32:1 (1977), 1–14  mathnet  crossref  mathscinet  zmath
    5. 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
    6. S. I. Adian, “The Burnside Problem on Periodic Groups, and Related Problems”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S2–S12  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. 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
    8. 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
    9. 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
    10. 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  elib  elib
    11. S. I. Adian, “New estimates of odd exponents of infinite Burnside groups”, Proc. Steklov Inst. Math., 289 (2015), 33–71  mathnet  crossref  crossref  isi  elib
    12. V. S. Atabekyan, L. D. Beklemishev, V. S. Guba, I. G. Lysenok, A. A. Razborov, A. L. Semenov, “Questions in algebra and mathematical logic. Scientific heritage of S. I. Adian”, Russian Math. Surveys, 76:1 (2021), 1–27  mathnet  crossref  crossref  mathscinet  isi  elib
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