The Automorphism Group of a Free Group
is not Subgroup Separable

to appear in:  Knots, Braids, and Mapping Class Groups Conference Proceedings.

Oliver T. Dasbach, Brian Mangum


Abstract:

 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 Bn,   n > 3,  are not
subgroup separable. In contrast, the groups B2 and B3 are well-known to
have this property.


Keywords:

LERF, subgroup separable, automorphism group of a free group,
braid groups
 


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