Automorphisms in Certain Nilpotent-by-Abelian Varieties of Groups

Abstract

Abstract For positive integers n and k , with $$n \ge 4$$ n ≥ 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.