✦ LIBER ✦

Some Representations of Groups of Automorphisms of a Free Group

✍ Scribed by Roger C. Alperin; Claudio Procesi

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 146 KB
Volume: 181
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0107

No coin nor oath required. For personal study only.

✦ Synopsis

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 Magnus᎐Gassner representations.

📜 SIMILAR VOLUMES

Automorphisms of Automorphism Groups of

Automorphisms of Automorphism Groups of Free Groups

✍ Martin R. Bridson; Karen Vogtmann 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 87 KB

If n G 3 and F is free of rank n, then Out Aut F s Out Out F s 1 . n n n ᮊ 2000 Academic Press n is an isomorphism. Tits's theorem leads to a proof that the outer automor-

Regular representations of finite groups

Regular representations of finite groups as automorphism groups of k-tournaments

✍ S. Marshall 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 104 KB

## Abstract It was shown by Babai and Imrich [2] that every finite group of odd order except $Z^2\_3$ and $Z^3\_3$ admits a regular representation as the automorphism group of a tournament. Here, we show that for __k__ ≥ 3, every finite group whose order is relatively prime to and strictly larger t

On Automorphism-Fixed Subgroups of a Fre

On Automorphism-Fixed Subgroups of a Free Group

✍ A. Martino; E. Ventura 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 101 KB

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 Automorphisms of a Fr

The Pure Symmetric Automorphisms of a Free Group Form a Duality Group

✍ Noel Brady; Jon McCammond; John Meier; Andy Miller 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 177 KB

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.

The Automorphism Groups of Relatively Fr

The Automorphism Groups of Relatively Free Algebras

✍ R.M. Bryant; V.A. Roman'kov 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 171 KB

On the Automorphism Group of a Free Pro-

On the Automorphism Group of a Free Pro-l Meta-abelian Group and an Application to Galois Representations

✍ Hiroshi Tsunogai 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 431 KB

## Abstract In § l of this article, we study group‐theoretical properties of some automorphism group Ψ^\*^ of the meta‐abelian quotient § of a free pro‐__l__ group § of rank two, and show that the conjugacy class of some element of order two of Ψ^\*^ is not determined by the action induced on the a