Geodesic
The abstract commensurator of Baumslag--Solitar groups
Algebra i logika, Tome 52 (2013) no. 1, pp. 64-83.

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Presentations are found for automorphism groups of all subgroups of finite index in the Baumslag–Solitar group with coprime integer parameters not equal to $0,1$, and $-1$. An abstract commensurator of Baumslag–Solitar groups with the same parameters is described.
Keywords: Baumslag–Solitar group, subgroup of finite index, abstract commensurator
Mots-clés : automorphism group. 
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F. A. Dudkin. The abstract commensurator of Baumslag--Solitar groups. Algebra i logika, Tome 52 (2013) no. 1, pp. 64-83. http://geodesic.mathdoc.fr/item/AL_2013_52_1_a4/

[1] N. V. Ivanov, “Automorphisms of complexes of curves and of Teichmuller spaces”, Int. Math. Res. Not., 1997:14 (1997), 651–666 | DOI | MR | Zbl

[2] B. Farb, M. Handel, “Commensurations of $\mathrm{Out}(F_n)$”, Publ. Math. Inst. Hautes Etud. Sci., 105 (2007), 1–48 | DOI | MR | Zbl

[3] C. J. Leininger, D. Margalit, “Abstract commensurators of braid groups”, J. Algebra, 299:2 (2006), 447–455 | DOI | MR | Zbl

[4] M. Ershov, “On the commensurator of the Nottingham group”, Trans. Am. Math. Soc., 362:12 (2010), 6663–6678 | DOI | MR | Zbl

[5] G. Baumslag, D. Solitar, “Some two-generator one-relator non-Hopfian groups”, Bull. Am. Math. Soc., 68:3 (1962), 199–201 | DOI | MR | Zbl

[6] J.-P. Serre, Trees, Springer-Verlag, Berlin–Heidelberg–New York, 1980 | MR | Zbl

[7] H. Bass, “Covering theory for graphs of groups”, J. Pure Appl. Algebra, 89:1–2 (1993), 3–47 | DOI | MR | Zbl

[8] F. A. Dudkin, “Podgruppy konechnogo indeksa v gruppakh Baumslaga–Solitera”, Algebra i logika, 49:3 (2010), 331–345 | MR | Zbl

[9] D. J. Collins, “The automorphism towers of some one-relator groups”, J. Lond. Math. Soc. III Ser., 36:3 (1978), 480–493 | DOI | MR | Zbl

[10] O. Bogopolski, “Abstract commensurators of solvable Baumslag–Solitar groups”, Commun. Algebra, 40:7 (2012), 2494–2502 | DOI | MR | Zbl

[11] R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980 | MR

[12] N. D. Gilbert, J. Howie, V. Metaftsis, E. Raptis, “Tree actions of automorphism groups”, J. Group Theory, 3:2 (2000), 213–223 | DOI | MR | Zbl