TY - JOUR
T1 - On asymptotic properties of verbal subsets in a group
AU - Myasnikov, A.
AU - Roman’kov, V.
N1 - Publisher Copyright:
© 2015, Pleiades Publishing, Ltd.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - We prove that the asymptotic density ρ(w[Fr]) of the verbal set w[Fr] in a free group Fr, r ≥ 2, is equal to 0 for every word w with exponent sum exp(w) ≠ 1. When exp(w) = 1 one has w[Fr] = Fr, and so ρ(w[Fr]) = 1.
AB - We prove that the asymptotic density ρ(w[Fr]) of the verbal set w[Fr] in a free group Fr, r ≥ 2, is equal to 0 for every word w with exponent sum exp(w) ≠ 1. When exp(w) = 1 one has w[Fr] = Fr, and so ρ(w[Fr]) = 1.
KW - asymptotic density
KW - free group
KW - verbal set
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U2 - 10.1134/S1995080215040113
DO - 10.1134/S1995080215040113
M3 - Article
AN - SCOPUS:84949186815
SN - 1995-0802
VL - 36
SP - 399
EP - 402
JO - Lobachevskii Journal of Mathematics
JF - Lobachevskii Journal of Mathematics
IS - 4
ER -