Automorphisms of Metabelian Groups

Papistas, Athanassios I.

Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 98-104

Résumé

We investigate the problem of determining when $\text{IA}({{F}_{n}}({{\mathbf{A}}_{m}}\mathbf{A}))$ is finitely generated for all $n$ and $m$ , with $n\ge 2$ and $m\ne 1$ . If $m$ is a nonsquare free integer then $\text{IA}({{F}_{n}}({{\mathbf{A}}_{m}}\mathbf{A}))$ is not finitely generated for all $n$ and if $m$ square free integer then $\text{IA}({{F}_{n}}({{\mathbf{A}}_{m}}\mathbf{A}))$ is finitely generated for all $n$ , with $n\ne 3$ , and $\text{IA}({{F}_{3}}({{\mathbf{A}}_{m}}\mathbf{A}))$ is not finitely generated. In case $m$ is square free, Bachmuth and Mochizuki claimed in ([7], Problem 4) that $\text{TR}({{\mathbf{A}}_{m}}\mathbf{A})$ is 1 or 4. We correct their assertion by proving that $\text{TR}({{\mathbf{A}}_{m}}\mathbf{A})=\infty$ .

Détail

DOI : 10.4153/CMB-1998-015-7

Mots-clés : 20F28