Automorphisms in Certain Nilpotent-by-Abelian Varieties of Groups

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2024年3月20日

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C. E. Kofinas

摘要

For positive integers n and k, with $n \ge 4$ $n \geq 4$ , let $F_{n}$ $F_{n}$ be the free group of rank n and let $G_{n,k} = F_{n}/\gamma _{3}(F^{\prime }_{n})[F^{\prime \prime }_{n},~_{k}F_{n}]$ $G_{n, k} = F_{n} / γ_{3} (F_{n}^{'}) [F_{n}^{″},_{k} F_{n}]$ . We show that for sufficiently large n, the automorphism group ${\textrm{Aut}}(G_{n,k})$ $Aut (G_{n, k})$ of $G_{n,k}$ $G_{n, k}$ is generated by the tame automorphisms and one more non-tame automorphism.