###
Subgroup
classification in Out(F_{n})

#### Lee Mosher, Rutgers University, Newark

For any subgroup H of Out(F_{n}), either H has a finite index subgroup that
fixes the conjugacy class of some proper, nontrivial free factor of
F_{n},
or H contains a fully irreducible element phi, meaning that no positive
power of phi fixes the conjugacy class of any proper, nontrivial free
factor of F_{n}.