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Mat. Zametki, 2009, Volume 86, Issue 4, Pages 483–490 (Mi mz8509)  

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

Monomorphisms of Free Burnside Groups

V. S. Atabekyan

Yerevan State University

Abstract: In the paper, it is proved that, for any odd $n\ge1039$, there are words $u(x,y)$ and $v(x,y)$ over the group alphabet $\{x,y\}$ such that, if $a$ and $b$ are any two noncommuting elements of the free Burnside group $B(m,n)$, then, for some $k$, the elements $u(a^k,b)$ and $v(a^k,b)$ freely generate a free Burnside subgroup of the group $B(m,n)$. In particular, the facts proved in the paper imply the uniform nonamenability of the group $B(m,n)$ for odd $n$, $n\ge1039$.

Keywords: absolutely free group, free Burnside group, uniformly nonamenable group, residually finite group, $2$-generated subgroup, Tarski monster, Hopfian group

DOI: https://doi.org/10.4213/mzm8509

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English version:
Mathematical Notes, 2009, 86:4, 457–462

Bibliographic databases:

UDC: 512.543
Received: 10.04.2009

Citation: V. S. Atabekyan, “Monomorphisms of Free Burnside Groups”, Mat. Zametki, 86:4 (2009), 483–490; Math. Notes, 86:4 (2009), 457–462

Citation in format AMSBIB
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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. 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
    2. A. S. Pahlevanyan, “Independent pairs in free Burnside groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 2, 58–62  mathnet
    3. 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
    4. Atabekyan V.S., “On Cep-Subgroups of N-Periodic Products”, J. Contemp. Math. Anal.-Armen. Aca., 46:5 (2011), 237–242  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. 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  scopus
    7. Adian S.I. Atabekyan V.S., “Periodic Products of Groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:3 (2017), 111–117  crossref  mathscinet  zmath  isi  scopus
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