Geodesic
Automorphisms of some cyclic extensions of free groups of rank three
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1400-1413 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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E. A. Shaporina. Automorphisms of some cyclic extensions of free groups of rank three. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1400-1413. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a15/

[1] O. Bogopolski, A. Martino, E. Ventura, “The automorphism group of a free-by-cyclic group in rank 2”, Commun. Algebra, 35:5 (2007), 1675–1690 | DOI | Zbl

[2] S.M. Gersten, “The automorphism group of a free group is not a CAT(0) group”, Proc. Am. Math. Soc., 121:4 (1994), 999–1002 | Zbl

[3] N. Brady, I. Soroko, “Dehn functions of subgroups of right-angled Artin groups”, Geom. Dedicata, 200 (2019), 197–239 | DOI | Zbl

[4] J.O. Button, “Tubular groups, 1-relator groups and nonpositive curvature”, Int. J. Algebra Comput., 29:8 (2019), 1367–1381 | DOI | Zbl

[5] N. Hoda, D.T. Wise, D.J. Woodhouse, “Residually finite tubular groups”, Proc. R. Soc. Edinb., Sect. A, Math., 150:6 (2020), 2937–2951 | DOI | Zbl

[6] J. McCool, “On basis-conjugating automorphisms of free groups”, Can. J. Math., 38:6 (1986), 1525–1529 | DOI | Zbl

[7] F.A. Dudkin, E.A. Shaporina, “Automorphisms of the Gersten Group”, Sib. Math. J., 62:3 (2021), 413–422 | DOI | Zbl

[8] R.C. Lyndon, P.E. Schupp, Combinatorial group theory, Springer, Berlin etc., 1977 | Zbl