A property of subgroups of infinite index in a free group

Arzhantseva, G.

doi:10.1090/S0002-9939-00-05508-8

A property of subgroups of infinite index in a free group
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Proc. Amer. Math. Soc. 128 (2000), 3205-3210 Request permission

Abstract:

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

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