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Fundam. Prikl. Mat., 2010, Volume 16, Issue 8, Pages 189–221 (Mi fpm1382)  

This article is cited in 2 scientific papers (total in 2 papers)

Amalgamated products of groups: measures of random normal forms

A. G. Myasnikova, V. N. Remeslennikovb, E. V. Frenkelc

a Stevens Institute of Technology, USA
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
c M. V. Lomonosov Moscow State University

Abstract: Let $G=\mathop{A\ast B}\limits_C$ be an amalgamated product of finite rank free groups $A,B$, and $C$. We introduce atomic measures and corresponding asymptotic densities on a set of normal forms of elements in $G$. We also define two strata of normal forms: the first one consists of regular (or stable) normal forms, and the second stratum is formed by singular (or unstable) normal forms. In a series of previous works about classical algorithmic problems, it was shown that standard algorithms work fast on elements of the first stratum and nothing is known about their work on the second stratum. In this paper, we give probabilistic and asymptotic estimates of these strata.

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English version:
Journal of Mathematical Sciences (New York), 2012, 185:2, 300–320

Bibliographic databases:

UDC: 512.54.0+510.53

Citation: A. G. Myasnikov, V. N. Remeslennikov, E. V. Frenkel, “Amalgamated products of groups: measures of random normal forms”, Fundam. Prikl. Mat., 16:8 (2010), 189–221; J. Math. Sci., 185:2 (2012), 300–320

Citation in format AMSBIB
\Bibitem{MyaRemFre10}
\by A.~G.~Myasnikov, V.~N.~Remeslennikov, E.~V.~Frenkel
\paper Amalgamated products of groups: measures of random normal forms
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 8
\pages 189--221
\mathnet{http://mi.mathnet.ru/fpm1382}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2869838}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 185
\issue 2
\pages 300--320
\crossref{https://doi.org/10.1007/s10958-012-0915-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866307431}


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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. A. G. Myasnikov, V. N. Remeslennikov, E. V. Frenkel, “Amalgamated Free Product of Groups: Normal Forms and Measures”, Math. Notes, 91:4 (2012), 592–596  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Frenkel E., Remeslennikov V.N., “Measuring Cones and Other Thick Subsets in Free Groups”, Int. J. Group Theory, 7:4 (2018), 27–40  crossref  mathscinet  isi  scopus
  • Фундаментальная и прикладная математика
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