Аннотация:

Description of the group of outer automorphisms of the Gersten group was obtained by the author together with F. Dudkin in 2021 [7]. In this paper, we study the possibility of extending the methods of that work to an infinite class of cyclic extensions of a free group of rank three 

$$G_k = \langle a, b, c, t | a^t = a, b^t = ba^k, 
c^t = c \rangle.$$

We have found the generating elements of the group $Out(G_k)$ and obtained a description of the structure of this group.