The Automorphism Group of a Free Group
is not Subgroup Separable
to appear in: Knots, Braids, and Mapping
Class Groups Conference Proceedings.
By a classical result of Gilbert Baumslag, the automorphism
group Aut(G) of a
finitely generated residually finite group G is residually finite.
While this implies
that the automorphism group of a free group Fn of
finite rank is residually
finite, the aim of this paper is to show that, for a (non-abelian)
free group, this
group is not subgroup separable.
As a corollary of our proof, we will get that the braid groups
n > 3, are not
subgroup separable. In contrast, the groups B2 and
are well-known to
have this property.
LERF, subgroup separable, automorphism group of a free group,