TY - JOUR
T1 - Amalgamated products of groups
T2 - Measures of random normal forms
AU - Myasnikov, A. G.
AU - Remeslennikov, V. N.
AU - Frenkel, E. V.
PY - 2012/8
Y1 - 2012/8
N2 - Let G = A *C B 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.
AB - Let G = A *C B 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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U2 - 10.1007/s10958-012-0915-z
DO - 10.1007/s10958-012-0915-z
M3 - Article
AN - SCOPUS:84866307431
SN - 1072-3374
VL - 185
SP - 300
EP - 320
JO - Journal of Mathematical Sciences (United States)
JF - Journal of Mathematical Sciences (United States)
IS - 2
ER -