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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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http://mi.mathnet.ru/eng/mz8509https://doi.org/10.4213/mzm8509 http://mi.mathnet.ru/eng/mz/v86/i4/p483
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
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This publication is cited in the following articles:
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S. I. Adian, “The Burnside problem and related topics”, Russian Math. Surveys, 65:5 (2010), 805–855
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A. S. Pahlevanyan, “Independent pairs in free Burnside groups”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 2, 58–62
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V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24
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Atabekyan V.S., “On Cep-Subgroups of N-Periodic Products”, J. Contemp. Math. Anal.-Armen. Aca., 46:5 (2011), 237–242
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S. I. Adian, Varuzhan Atabekyan, “Characteristic properties and uniform non-amenability of $n$-periodic products of groups”, Izv. Math., 79:6 (2015), 1097–1110
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Atabekyan V.S., “the Automorphisms of Endomorphism Semigroups of Free Burnside Groups”, Int. J. Algebr. Comput., 25:4 (2015), 669–674
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Adian S.I. Atabekyan V.S., “Periodic Products of Groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:3 (2017), 111–117
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