A property of subgroups of infinite index in a free group

Author:

Arzhantseva G.

Abstract

We prove that if H H is a finitely generated subgroup of infinite index in a free group F m F_m , then, in a certain statistical meaning, the normal subgroup generated by “randomly” chosen elements r 1 , , r n r_1,\dots ,r_n of F m F_m has trivial intersection with H H .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference7 articles.

1. Generality of the class of groups in which subgroups with a lesser number of generators are free;Arzhantseva, G. N.;Mat. Zametki,1996

2. G. N. Arzhantseva, On the groups all of whose subgroups with fixed number of generators are free, Fundamental and Applied Mathematics, 3(3) (1997), 675-683 (in Russian).

3. Discrete groups of motions;Greenberg, Leon;Canadian J. Math.,1960

4. On finitely generated subgroups of a free group;Karrass, Abraham;Proc. Amer. Math. Soc.,1969

5. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89;Lyndon, Roger C.,1977

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