## Advanced Studies in Pure Mathematics

### Amalgamations and automorphism groups

David Wright

#### Abstract

Many types of automorphism groups in algebra have nice structures arising from actions on combinatoric spaces. We recount some examples including Nagao's Theorem, the Jung-Van der Kulk Theorem, and a new structure theorem for the tame subgroup $\text{TA}_3(K)$ of the group $\text{GA}_3(K)$ of polynomial automorphisms of $\mathbb{A}_K^3$, for $K$ a field of characteristic zero. We also ask whether a larger collection of automorphism groups possess a similar kind of structure.

#### Article information

Dates
Revised: 14 June 2016
First available in Project Euclid: 21 September 2018

https://projecteuclid.org/ euclid.aspm/1537498716

Digital Object Identifier
doi:10.2969/aspm/07510465

Mathematical Reviews number (MathSciNet)
MR3793373

Zentralblatt MATH identifier
1396.14063

#### Citation

Wright, David. Amalgamations and automorphism groups. Algebraic Varieties and Automorphism Groups, 465--474, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510465. https://projecteuclid.org/euclid.aspm/1537498716