Subgroup separability of graphs of abelian groups

Proceedings of the American Mathematical Society

Volumn 132, Issue 7, 2004, Pages 1873-1884

  Metaftsis, V ^a   Raptis, E ^b  

^a UNIVERSITY OF THE AEGEAN   (Greece)

^b UNIVERSITY OF ATHENS   (Greece)

Author keywords

Graphs of groups; HNN extensions; Residually finite groups; Subgroup separable groups (LERF)

Indexed keywords

EID: 2942677183     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-03-07287-3     Document Type: Conference Paper

References (20)

1. R.B.J.T. Allenby and D. Doniz, A free product of finitely generated nilpotent groups amalgamating a cycle that is not subgroup separable, Proc. Amer. Math. Soc. 124, 1003-1005 (1996). MR 97a:20049
2. R.B.J.T. Allenby and R. J. Gregorac, On locally extended residually finite groups, Lecture Notes In Mathematics, Vol. 319, Springer-Verlag, Berlin, 1973, pp. 9-17. MR 52:3333
3. S. Andreadakis, E. Raptis, and D. Varsos, A characterisation of residually finite HNN-extensions of finitely generated abelian groups, Arch. Math. (Basel) 50, 495-501 (1988). MR 89g:20046
4. M. Bestvina and N. Brady, Morse theory and finiteness properties of groups. Invent. Math. 129, 445-470 (1997). MR 98i:20039
5. A. Blass and P. M. Neumann, An application of universal algebra in group theory, Michigan Math. J. 21, 167-169 (1974). MR 51:729
6. R. G. Burns, A. Karrass, and D. Solitar, A note on groups with separable finitely generated subgroups, Bull. Austral. Math. Soc. 36, 153-160 (1987). MR 88g:20057
7. D. E. Cohen, Combinatorial group theory: a topological approach. London Mathematical Society Student Texts 14, 1989. MR 91d:20001
8. R. Gitik, Graphs and separability properties of groups, J. Algebra 188, 125-143 (1997). MR 98e:20033
9. a = b B to be LERF, Israel J. Math. 73, 123-125 (1991). MR 92g:20046
10. M. Hall, Jr., Coset representations in free groups, Trans. Amer. Math. Soc. 87, 421-432 (1949). MR 11:322e
11. D. D. Long and G. A. Niblo, Subgroup separability and 3-manifold groups, Math. Z. 207, 209-215 (1991). MR 92g:20047
12. V. Metaftsis and E. Raptis, Subgroup separability of HNN-extensions with abelian base group, J. Algebra 245, 42-49 (2001). MR 2002j:20050
13. K. A. Mihailova, The occurrence problem for direct products of groups, Mat. Sbornik 70, 241-251 (1966). MR 33:2707
14. G. Niblo and D. Wise, Subgroup separability, knot groups and graph manifolds, Proc. Amer. Math. Soc. 129, 685-693 (2001). MR 2001f:20075
15. J.-P. Serre, Trees, Springer-Verlag, Berlin and New York, 1980. MR 82c:20083
16. P. Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. 17, 555-565 (1978). MR 58:12996
17. P. Scott, Correction to "Subgroups of surface groups are almost geometric", J. London Math. Soc. 32, 217-220 (1985). MR 87k:57003
18. P. B. Shalen, Three-manifolds and Baumslag-Solitar groups, Geometric Topology and Geometric Group Theory (Milwaukee, WI, 1997). Topology Appl. 110, 113-118 (2001). MR 2001j:57002
19. P. B. Shalen, Three-manifolds and Baumslag-Solitar groups, Geometric Topology and Geometric Group Theory (Milwaukee, WI, 1997). Topology Appl. 110, 113-118 (2001). MR 2001j:57002
20. D. T. Wise, Subgroup separability of graphs of free groups with cyclic edge groups, Quart. J. Math. 51, 107-129 (2000). MR 2001e:20026