Solvable subgroups of Out(Fn) are virtually Abelian

被引：21

作者：

Bestvina, M

Feighn, M

Handel, M

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[2] Rutgers State Univ, Dept Math, Newark, NJ 07102 USA

[3] CUNY Herbert H Lehman Coll, Dept Math & Comp Sci, Bronx, NY 10468 USA

来源：

GEOMETRIAE DEDICATA | 2004年 / 104卷 / 01期

基金：

美国国家科学基金会;

关键词：

free group; outer automorphism; solvable; relative train track;

D O I：

10.1023/B:GEOM.0000022864.30278.34

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F-n be the free group of rank n, let Aut(F-n) be its automorphism group and let Out(F-n) be its outer automorphism group. We show that every solvable subgroup of Out(F-n) has a finite index subgroup that is finitely generated and free Abelian. We also show that every Abelian subgroup of Out(F-n) has a finite index subgroup that lifts to Aut(F-n).

引用

页码：71 / 96

页数：26

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