494
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

A Bass–Serre theoretic proof of a theorem of Romanovskii and Burns

ORCID Icon
Pages 2004-2013 | Received 06 Sep 2021, Accepted 05 Sep 2022, Published online: 08 Dec 2022

References

  • Antolín, Y., Martino, A., Schwabrow, I. (2014). Kurosh rank of intersections of subgroups of free products of right-orderable groups. Math. Res. Lett. 21(4):649–661. DOI: 10.4310/MRL.2014.v21.n4.a2.
  • Bass, H. (1993). Covering theory for graphs of groups. J. Pure Appl. Algebra 89(1–2):3–47. DOI: 10.1016/0022-4049(93)90085-8.
  • Burns, R. G. (1969). A note on free groups. Proc. Amer. Math. Soc. 23:14–17. DOI: 10.2307/2037477.
  • Burns, R. G. (1971). On finitely generated subgroups of free products. J. Austral. Math. Soc. 12:358–364. DOI: 10.1017/S1446788700009824.
  • Gitik, R. (1997). Graphs and separability properties of groups. J. Algebra 188(1):125–143. DOI: 10.1006/jabr.1996.6847.
  • Gruschko, I. (1940). Über die Basen eines freien Produktes von Gruppen. Rec. Math. [Mat. Sbornik] N.S. 8(50):169–182.
  • Hall, M., Jr. (1949). Coset representations in free groups. Trans. Amer. Math. Soc. 67:421–432. DOI: 10.2307/1990483.
  • Kurosch, A. (1934). Die Untergruppen der freien Produkte von beliebigen Gruppen. Math. Ann. 109(1):647–660. DOI: 10.1007/BF01449159.
  • Romanovskiĭ, N. S. (1969). On the residual finiteness of free products with respect to subgroups. Izv. Akad. Nauk SSSR Ser. Mat. 33:1324–1329.
  • Serre, J.-P. (2003). Trees. Springer Monographs in Mathematics. Berlin: Springer-Verlag. Translated from the French original by John Stillwell, Corrected 2nd printing of the 1980 English translation.
  • Stallings, J. R. (1983). Topology of finite graphs. Invent. Math. 71(3):551–565. DOI: 10.1007/BF02095993.
  • Wilton, H. (2007). Elementarily free groups are subgroup separable. Proc. Lond. Math. Soc. (3) 95(2):473–496. DOI: 10.1112/plms/pdm020.