Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

# Automorphisms of metabelian groups

Published:1998-03-01
Printed: Mar 1998
• Athanassios I. Papistas
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

We investigate the problem of determining when $\IA (F_{n}({\bf A}_{m}{\bf A}))$ is finitely generated for all $n$ and $m$, with $n\geq 2$ and $m\neq 1$. If $m$ is a nonsquare free integer then $\IA(F_{n}({\bf A}_{m}{\bf A}))$ is not finitely generated for all $n$ and if $m$ is a square free integer then $\IA(F_{n}({\bf A}_{m}{\bf A}))$ is finitely generated for all $n$, with $n\neq 3$, and $\IA(F_{3}({\bf A}_{m}{\bf A}))$ is not finitely generated. In case $m$ is square free, Bachmuth and Mochizuki claimed in ([7], Problem 4) that $\TR({\bf A}_{m}{\bf A})$ is $1$ or $4$. We correct their assertion by proving that $\TR({\bf A}_{m}{\bf A})=\infty$.
 MSC Classifications: 20F28 - Automorphism groups of groups [See also 20E36]

© Canadian Mathematical Society, 2015 : https://cms.math.ca/