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Solvable Subgroups of Out(F n ) are Virtually Abelian |
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| Authors: | Mladen Bestvina Mark Feighn Michael Handel |
| Affiliation: | (1) Department of Mathematics, University of Utah, 155 South 1400 East, 233, Salt Lake City, UT, 84112, U.S.A;(2) Mathematics Department, Rutgers University, Newark, NJ, 07102, U.S.A;(3) Mathematics and Computer Science Department, Lehman College, City University of New York, 250 Bedford Park Boulevard West, Bronx, NY, 10468-1589, U.S.A |
| Abstract: | Let Fn be the free group of rank n, let Aut(Fn) be its automorphism group and let Out(Fn) be its outer automorphism group. We show that every solvable subgroup of Out(Fn) has a finite index subgroup that is finitely generated and free Abelian. We also show that every Abelian subgroup of Out(Fn) has a finite index subgroup that lifts to Aut(Fn). |
| Keywords: | free group outer automorphism solvable relative train track |
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