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Automorphisms of metabelian groups

  Published:1998-03-01
 Printed: Mar 1998
  • Athanassios I. Papistas
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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 show english descriptions Automorphism groups of groups [See also 20E36] 20F28 - Automorphism groups of groups [See also 20E36]
 

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