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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 5, Pages 81–110 (Mi izv747)  

This article is cited in 1 scientific paper (total in 1 paper)

Burnside structures of finite subgroups

I. G. Lysenok

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We establish conditions guaranteeing that a group $B$ possesses the following property: there is a number $\ell$ such that if elements $w$, $x^{-1}wx$, …, $x^{-\ell+1}wx^{\ell-1}$ of $B$ generate a finite subgroup $G$ then $x$ lies in the normalizer of $G$. These conditions are of a quite special form. They hold for groups with relations of the form $x^n=1$ which appear as approximating groups for the free Burnside groups $B(m,n)$ of sufficiently large even exponent $n$. We extract an algebraic assertion which plays an important role in all known approaches to substantial results on the groups $B(m,n)$ of large even exponent, in particular, to proving their infiniteness. The main theorem asserts that when $n$ is divisible by 16, $B$ has the above property with $\ell=6$.

DOI: https://doi.org/10.4213/im747

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English version:
Izvestiya: Mathematics, 2007, 71:5, 939–965

Bibliographic databases:

UDC: 519.41
MSC: 20F50, 20E07
Received: 12.01.2006

Citation: I. G. Lysenok, “Burnside structures of finite subgroups”, Izv. RAN. Ser. Mat., 71:5 (2007), 81–110; Izv. Math., 71:5 (2007), 939–965

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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