Mathematical logic, algebra and number theory

Automorphisms of some cyclic extensions of free groups of rank three

E. A. Shaporina

Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia

Abstract: 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.

Keywords: Free group, split cyclic extension, group of outer automorphisms.

UDC: 512.54

MSC: 20E06

Received April 2, 2024, published December 18, 2024

Language: English

DOI: 10.33048/semi.2024.21.088