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Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 4, Pages 715–734 (Mi izv2442)  

This article is cited in 19 scientific papers (total in 21 papers)

Infinite irreducible systems of group identities

S. I. Adian

Abstract: In this paper we construct infinite irreducible systems of group identities in two variables. We also demonstrate the existence of a group defined by two generators and a countable set of identity relations in which the word problem is unsolvable.

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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:4, 721–739

Bibliographic databases:

UDC: 519.4
MSC: 20E10, 20F10, 20F05
Received: 26.02.1970

Citation: S. I. Adian, “Infinite irreducible systems of group identities”, Izv. Akad. Nauk SSSR Ser. Mat., 34:4 (1970), 715–734; Math. USSR-Izv., 4:4 (1970), 721–739

Citation in format AMSBIB
\by S.~I.~Adian
\paper Infinite irreducible systems of group identities
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1970
\vol 34
\issue 4
\pages 715--734
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 4
\pages 721--739

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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. Yu. G. Kleiman, “On a basis of the product of varieties of groups”, Math. USSR-Izv., 7:1 (1973), 91–94  mathnet  crossref  mathscinet  zmath
    2. Yu. I. Merzlyakov, “Chetvertyi Vsesoyuznyi simpozium po teorii grupp”, UMN, 28:3(171) (1973), 235–239  mathnet  mathscinet
    3. S. I. Adian, “An axiomatic method of constructing groups with given properties”, Russian Math. Surveys, 32:1 (1977), 1–14  mathnet  crossref  mathscinet  zmath
    4. Yu. G. Kleiman, “Some questions in the theory of varieties of groups”, Math. USSR-Izv., 22:1 (1984), 33–65  mathnet  crossref  mathscinet  zmath
    5. V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. 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
    7. 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
    8. 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
    9. A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. 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
    11. 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
    12. 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
    13. P. Modabberi, M. Shahryari, “Equational conditions in universal algebraic geometry”, Algebra and Logic, 55:2 (2016), 146–172  mathnet  crossref  crossref  isi
    14. S. I. Adian, V. S. Atabekyan, “On free groups in the infinitely based varieties of S. I. Adian”, Izv. Math., 81:5 (2017), 889–900  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    15. Atabekyan V.S. Aslanyan H.T., “The Automorphisms of Endomorphism Semigroups of Relatively Free Groups”, Int. J. Algebr. Comput., 28:2 (2018), 207–215  crossref  isi
    16. H. T. Aslanyan, “On automorphisms and endomorphisms of $CC$ groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:1 (2018), 60–63  mathnet
    17. Aslanyan H.T., Gevorgyan A.L., Grigoryan H.A., “Finite Subgroups of the Free Groups of the Infinitely Based Varieties of S. i. Adian”, Armen. J. Math., 11:6 (2019), 1–6  isi
    18. S. I. Adian, V. S. Atabekyan, “Normal Automorphisms of Free Groups of Infinitely Based Varieties”, Math. Notes, 108:2 (2020), 149–154  mathnet  crossref  crossref  mathscinet  isi  elib
    19. V. S. Atabekyan, “The set of $2$-genereted $C^*$-simple relatively free groups has the cardinality of the continuum”, Uch. zapiski EGU, ser. Fizika i Matematika, 54:2 (2020), 81–86  mathnet  crossref
    20. Gevorgyan A.L. Gevorgyan G.G., “Finite Subgroups of the Relatively Free N-Torsion Groups”, J. Contemp. Math. Anal.-Armen. Aca., 55:1 (2020), 1–4  crossref  isi
    21. 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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