CLASS-PRESERVING AUTOMORPHISMS OF CERTAIN HNN EXTENSIONS OF BAUMSLAG-SOLITAR GROUPS

Title & Authors
CLASS-PRESERVING AUTOMORPHISMS OF CERTAIN HNN EXTENSIONS OF BAUMSLAG-SOLITAR GROUPS
Kim, Goansu; Zhou, Wei;

Abstract
We show that, for any non-zero integers $\small{{\lambda}}$, $\small{{\mu}}$, $\small{{\nu}}$, $\small{{\xi}}$, class-preserving automorphisms of the group G({\lambda},{\mu},{\nu},{\xi})
Keywords
HNN extensions;residually finite;conjugacy separable;Baumslag-Solitar groups;
Language
English
Cited by
References
1.
R. B. J. T. Allenby, G. Kim, and C. Y. Tang, Residual finiteness of outer automorphism groups of finitely generated non-triangle Fuchsian groups, Internat. J. Algebra Comput. 15 (2005), no. 1, 59-72.

2.
R. B. J. T. Allenby, G. Kim, and C. Y. Tang, Outer automorphism groups of Seifert 3-manifold groups over non-orientable surfaces, J. Algebra 322 (2009), no. 4, 957-968.

3.
G. Baumslag, A non-cyclic one-relator group all of whose finite quotients are cyclic, J. Austral. Math. Soc. 10 (1969), 497-498.

4.
G. Baumslag and D. Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 38 (1962), 199-201.

5.
A. V. Borshchev and D. I. Moldavanskii, On the isomorphism of some groups with one defining relation, Math. Notes 79 (2006), no. 1-2, 31-40.

6.
A. M. Brunner, On a class of one-relator groups, Canad. J. Math. 32 (1980), no. 2, 414-420.

7.
W. Burnside, On the outer automorphisms of a group, Proc. London Math. Soc. 11 (1913), 40-42.

8.
D. J. Collins, Recursively enumerable degrees and the conjugacy problem, Acta Math. 122 (1969), 115-160.

9.
G. Endimioni, Pointwise inner automorphisms in a free nilpotent group, Q. J. Math. 53 (2002), no. 4, 397-402.

10.
B. Farb and L. Mosher, A rigidity theorem for the solvable Baumslag-Solitar groups (with an appendix by daryl cooper), Invent. Math. 131 (1998), no. 2, 419-451.

11.
B. Farb and L. Mosher, Quasi-isometric rigidity for the solvable Baumslag-Solitar groups II, Invent. Math. 137 (1999), no. 3, 613-649.

12.
S. M. Gersten, Isoperimetric and isodiametric functions of finite presentations, In Geometric group theory, Vol. 1 (Sussex, 1991), volume 181 of London Math. Soc. Lecture Note Ser. Cambridge Univ. Press, Cambridge, 1993.

13.
E. K. Grossman, On the residual finiteness of certain mapping class groups, J. London Math. Soc. (2) 9 (1974), 160-164.

14.
M. Kapovich and B. Kleiner, Coarse Alexander duality and duality groups, J. Differential Geom. 69 (2005), no. 2, 279-352.

15.
G. Kim and C. Y. Tang, A criterion for the conjugacy separability of certain HNN-extensions of groups, J. Algebra 222 (1999), no. 2, 574-594.

16.
G. Kim and C. Y. Tang, Residual finiteness of outer automorphism groups of certain 1-relator groups, Sci. China Ser. A 52 (2009), no. 2, 287-292.

17.
G. Kim and C. Y. Tang, Outer automorphism groups of certain 1-relator groups, Sci. China Math. 53 (2010), no. 6, 1635-1641.

18.
R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Ergebnisse der Mathematik Bd. 89. Springer-Verlag, Berlin-Heidelberg-New York, 1977.

19.
S. Meskin, Nonresidually finite one-relator groups, Trans. Amer. Math. Soc. 164 (1972), 105-114.

20.
V. Metaftsis and M. Sykiotis, On the residual finiteness of outer automorphisms of hyperbolic groups, Geom. Dedicata 117 (2006), 125-131.

21.
A. Myasnikov, A. Ushakova, and D. W. Won, The word problem in the Baumslag group with a non-elementary Dehn function is polynomial time decidable, J. Algebra 345 (2011), no. 1, 324-342.

22.
M. V. Neshchadim, Free products of groups that do not have outer normal automorphisms, Algebra and Logic 35 (1996), no. 5, 316-318.

23.
E. Raptis, O. Talelli, and D. Varsos, On the Hopficity of certain HNN-extensions with base a Baumslag-Solitar group, Algebra Coll. 9 (2002), no. 1, 39-48.

24.
D. Segal, On the outer automorphism group of a polycyclic group, In Proceedings of the Second International Group Theory Conference (Bressanone, 1989), Rend. Circ. Mat. Palermo (2) Suppl. (1990), no. 23, 265-278.

25.
D. Tieudjo and D. I. Moldavanskii, On the automorphisms of some one-relator groups, Comm. Algebra 6 (2006), no. 11, 3975-3983.

26.
G. E. Wall, Finite groups with class-preserving outer automorphisms, J. London Math. Soc. 22 (1947), 315-320.

27.
P. C. Wong and K. B. Wong, Residual finiteness of outer automorphism groups of certain tree products, J. Group Theory 10 (2007), no. 3, 389-400.

28.
P. C. Wong and K. B. Wong, Conjugacy separability and outer automorphism groups of certain HNN extensions, J. Algebra 334 (2011), 74-83.

29.
W. Zhou and G. Kim, Class-preserving automorphisms and inner automorphisms of certain tree products of groups, J. Algebra 341 (2011), 198-208.

30.
W. Zhou and G. Kim, Class-preserving automorphisms of generalized free products amalgamating a cyclic normal subgroup, Bull. Korean Math. Soc. 49 (2012), no. 5, 949-959.