Geodesic
Automorphisms of Metabelian Groups
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 98-104

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\text{TR}({{\mathbf{A}}_{m}}\mathbf{A})=\infty$ .
DOI : 10.4153/CMB-1998-015-7
Mots-clés : 20F28 
Papistas, Athanassios I. Automorphisms of Metabelian Groups. Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 98-104. doi: 10.4153/CMB-1998-015-7
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