Geodesic
Mutual embeddings of right-angled Artin groups and generalized Baumslag-Solitar groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 809-814.

Voir la notice de l'article provenant de la source Math-Net.Ru

A finitely generated group $G$ acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group ($GBS$ group). In this paper, we study when a given $GBS$ group can be embedded in a right-angled Artin group ($RAAG$) and vice versa. An exhaustive description has been obtained in both cases. If an embedding exists, then we discuss its construction.
Keywords: right-angled Artin group, generalized Baumslag–Solitar group, embedding problem. 
@article{SEMR_2022_19_2_a8,
     author = {F. A. Dudkin},
     title = {Mutual embeddings of right-angled {Artin} groups and generalized {Baumslag-Solitar} groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {809--814},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a8/}
}
TY  - JOUR
AU  - F. A. Dudkin
TI  - Mutual embeddings of right-angled Artin groups and generalized Baumslag-Solitar groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 809
EP  - 814
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a8/
LA  - en
ID  - SEMR_2022_19_2_a8
ER  - 
%0 Journal Article
%A F. A. Dudkin
%T Mutual embeddings of right-angled Artin groups and generalized Baumslag-Solitar groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 809-814
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a8/
%G en
%F SEMR_2022_19_2_a8
F. A. Dudkin. Mutual embeddings of right-angled Artin groups and generalized Baumslag-Solitar groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 809-814. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a8/

[1] A.J. Duncan, V.N. Remeslennikov, A.V. Treier, “A survey of free partially commutative groups”, J. Phys.: Conf. Ser., 1441 (2020), 012136 | DOI | MR

[2] J.P. Serre, Trees, Springer, Berlin etc, 1980 | MR | Zbl

[3] M. Clay, M. Forester, “On the isomorphism problem for generalized Baumslag-Solitar groups”, Algebr. Geom. Topol., 8:4 (2008), 2289–2322 | DOI | MR | Zbl

[4] D.J.S. Robinson, “Generalized Baumslag-Solitar groups: a survey of recent progress”, Groups St Andrews 2013, Selected papers of the conference (St. Andrews, UK, August 3-11, 2013), LMS, Lecture Note Series, 422, eds. Campbell C.M. (ed.) et al., Cambridge University Press, Cambridge, 2016, 457–469 | MR | Zbl

[5] G. Levitt, “Quotients and subgroups of Baumslag–Solitar groups”, J. Group Theory, 18:1 (2015), 1–43 | DOI | MR | Zbl

[6] F.A. Dudkin, “On the embedding problem for generalized Baumslag-Solitar groups”, J. Group Theory, 18:4 (2015), 655–684 | DOI | MR | Zbl

[7] S.-H Kim, T. Koberda, “Embedability between right-angled Artin groups”, Geom. Topol., 17:1 (2013), 493–530 | DOI | MR | Zbl

[8] M. Forester, “Deformation and rigidity of simplicial group actions on trees”, Geom. Topol., 6 (2002), 219–267 | DOI | MR | Zbl

[9] G. Levitt, “Generalized Baumslag-Solitar groups: rank and finite index subgroups”, Ann. Inst. Fourier, 65:2 (2015), 725–762 | DOI | MR | Zbl

[10] G. Duchamp, D. Krob, “The lower central series of the free partially commutative group”, Semigroup Forum, 45:3 (1992), 385–394 | DOI | MR | Zbl

[11] E.I. Timoshenko, “Mal'tsev bases for partially commutative nilpotent group”, Int. J. Algebra Comput., 32:1 (2022), 1–9 | DOI | MR | Zbl

[12] F.A. Dudkin, “$\mathcal{F}_\pi$-residuality of generalized Baumslag-Solitar groups”, Arch. Math., 114:2 (2020), 129–134 | DOI | MR | Zbl