Automorphisms of Automorphism Groups of Free Groups
โ Scribed by Martin R. Bridson; Karen Vogtmann
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 87 KB
- Volume
- 229
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
โฆ Synopsis
If n G 3 and F is free of rank n, then Out Aut F s Out Out F s 1 . n n n แฎ 2000 Academic Press n
is an isomorphism. Tits's theorem leads to a proof that the outer automor-
๐ SIMILAR VOLUMES
We show that the representations of certain automorphism groups of a free group afforded by compact Lie groups as described by Long can be decomposed into sums of trivial representations and MagnusแGassner representations.
We prove that if an endomorphism ฯ of a free group F n of a finite rank n preserves an automorphic orbit Orb AutF n W with W = 1, i.e., if ฯ Orb AutF n W โ Orb AutF n W , then ฯ is an automorphism. ๏ฃฉ 2002 Elsevier Science (USA)
Let F be a finitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-fixed, or auto-fixed for short, if there exists a set S of automorphisms of F such that H is precisely the set of elements fixed by every element of S; similarly, H is 1-auto-fixed if th
The pure symmetric automorphism group of a finitely generated free group consists of those automorphisms which send each standard generator to a conjugate of itself. We prove that these groups are duality groups.