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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 5, Pages 3–36 (Mi izv2633)  

This article is cited in 17 scientific papers (total in 17 papers)

On subgroups of free Burnside groups of odd exponent $n\ge 1003$

V. S. Atabekian

Yerevan State University

Abstract: We prove that for any odd number $n\ge 1003$, every non-cyclic subgroup of the 2-generator free Burnside group of exponent $n$ contains a subgroup isomorphic to the free Burnside group of exponent $n$ and infinite rank. Various families of relatively free $n$-periodic subgroups are constructed in free periodic groups of odd exponent $n\ge 665$. For the same groups, we describe a monomorphism $\tau$ such that a word $A$ is an elementary period of rank $\alpha$ if and only if its image $\tau(A)$ is an elementary period of rank $\alpha+1$.

Keywords: free Burnside group, variety of periodic groups, group with cyclic subgroups, periodic word, reduced word.


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English version:
Izvestiya: Mathematics, 2009, 73:5, 861–892

Bibliographic databases:

UDC: 512.543+512.544
MSC: 20F50, 20F05
Received: 12.03.2007

Citation: V. S. Atabekian, “On subgroups of free Burnside groups of odd exponent $n\ge 1003$”, Izv. RAN. Ser. Mat., 73:5 (2009), 3–36; Izv. Math., 73:5 (2009), 861–892

Citation in format AMSBIB
\by V.~S.~Atabekian
\paper On subgroups of free Burnside groups of odd exponent $n\ge 1003$
\jour Izv. RAN. Ser. Mat.
\yr 2009
\vol 73
\issue 5
\pages 3--36
\jour Izv. Math.
\yr 2009
\vol 73
\issue 5
\pages 861--892

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    This publication is cited in the following articles:
    1. V. S. Atabekyan, “Monomorphisms of Free Burnside Groups”, Math. Notes, 86:4 (2009), 457–462  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. 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
    3. V. S. Atabekyan, “Nonunitarizable Periodic Groups”, Math. Notes, 87:6 (2010), 908–911  mathnet  crossref  crossref  mathscinet  isi
    4. 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
    5. A. S. Pahlevanyan, “Independent pairs in free Burnside groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 2, 58–62  mathnet
    6. H. R. Rostami, “Non-unitarizable groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 3, 40–43  mathnet
    7. 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
    8. Atabekyan V.S., “On CEP-subgroups of $n$-periodic products”, J. Contemp. Math. Anal., 46:5 (2011), 237–242  crossref  mathscinet  zmath  isi
    9. Atabekyan V.S., “The Groups of Automorphisms Are Complete for Free Burnside Groups of Odd Exponents N >= 1003”, Int. J. Algebr. Comput., 23:6 (2013), 1485–1496  crossref  mathscinet  zmath  isi  elib
    10. V. S. Atabekyan, “The automorphism tower problem for free periodic groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2013, no. 2, 3–7  mathnet
    11. V. S. Atabekyan, “Automorphism groups and endomorphism semigroups of groups $B(m,n)$”, Algebra and Logic, 54:1 (2015), 58–62  mathnet  crossref  crossref  mathscinet  isi
    12. S. I. Adian, Varuzhan Atabekyan, “Characteristic properties and uniform non-amenability of $n$-periodic products of groups”, Izv. Math., 79:6 (2015), 1097–1110  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. Atabekyan V.S., “the Automorphisms of Endomorphism Semigroups of Free Burnside Groups”, Int. J. Algebr. Comput., 25:4 (2015), 669–674  crossref  mathscinet  zmath  isi  elib
    14. Button J.O., “Groups and Embeddings in Sl(2, C)”, Commun. Algebr., 44:1 (2016), 265–278  crossref  mathscinet  zmath  isi
    15. S. I. Adian, V. S. Atabekyan, “$C^*$-Simplicity of $n$-Periodic Products”, Math. Notes, 99:5 (2016), 631–635  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. Atabekyan V.S., Gevorgyan A.L., Stepanyan Sh.A., “The Unique Trace Property of N-Periodic Product of Groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:4 (2017), 161–165  crossref  mathscinet  zmath  isi
    17. 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
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