Given a free factor A of the rank n free group F_n, we characterize when the
subgroup of Out(F_n) that stabilizes the conjugacy class of A is distorted in
Out(F_n). We also prove that the image of the natural embedding of Aut(F_{n-1})
in Aut(F_n) is nondistorted, that the stabilizer in Out(F_n) of the conjugacy
class of any free splitting of F_n is nondistorted, and we characterize when
the stabilizer of the conjugacy class of an arbitrary free factor system of F_n
is distorted. In all proofs of nondistortion, we prove the stronger statement
that the subgroup in question is a Lipschitz retract. As applications we
determine Dehn functions and automaticity for Out(F_n) and Aut(F_n).Comment: Version 3: 35 pages. Revised for publication. Changes from previous
versions: significant economies in exposition. Added an explicit description
of the stabilizer of a free splitting, in Lemma 1
