Automorphisms of Relatively Free Groups in the Variety N 2 A ∧ AN 2 ∧ N c

For positive integers n and c , with n ⩾ 2, let G n , c be a relatively free group of finite rank n in the variety N 2 A ∧ AN 2 ∧ N c . It is shown that the subgroup of the automorphism group Aut( G n , c ) of G n , c generated by the tame automorphisms and an explicitly described finite set of IA‐automorphisms of G n , c has finite index in Aut( G n , c ). Furthermore, it is proved that there are no non‐trivial elements of G n , c fixed by every tame automorphism of G n , c .