Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SEPARABILITY PROPERTIES OF CERTAIN POLYGONAL PRODUCTS OF GROUPS

  • Published : 2002.05.01
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Abstract

Let G = E${\ast}_{A}F$, where A is a finitely generated abelian subgroup. We prove a criterion for G to be {A}-double coset separable. Applying this result, we show that polygonal products of central subgroup separable groups, amalgamating trivial intersecting central subgroups, are double coset separable relative to certain central subgroups of their vertex groups. Finally we show that such polygonal products are conjugacy separable. It follows that polygonal products of polycyclic-by-finite groups, amalgamating trivial intersecting central subgroups, are conjugacy separable.

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References

  1. Canad. Math. Bull. v.32 no.1 On the residual finiteness of certain polygonal products R. B. J. T. Allenby;C. Y. Tang https://doi.org/10.4153/CMB-1989-002-8
  2. J. Austral. Math. Soc. Ser. A v.29 no.1 Separating conjugates in amalgamated free products and HNN extensions J. L. Dyer https://doi.org/10.1017/S1446788700020917
  3. Contemp. Math., Amer. Math. Soc. v.109 Conjugacy separability of Fuchsion groups and related questions B. Fine;G. Rosenberger https://doi.org/10.1090/conm/109/1076372
  4. J. Algebra v.42 Conjugacy separability in polycyclic groups E. Formanek https://doi.org/10.1016/0021-8693(76)90021-1
  5. Ph. D. thesis Graph Products of Groups E. R. Green
  6. Trans. Amer. Math. Soc. v.67 Coset representations in free groups M. Hall, Jr. https://doi.org/10.2307/1990483
  7. J. London Math. Soc. v.26 A finitely generated infinite simple group G. Higman https://doi.org/10.1112/jlms/s1-26.1.61
  8. Michigan Math. J. v.46 On linear and residual properties of graph products Tim Hsu;Daniel T. Wise https://doi.org/10.1307/mmj/1030132408
  9. Bull. Austral. Math. Soc. v.45 no.3 On polygonal products of finitely generated abelian groups G. Kim https://doi.org/10.1017/S0004972700030343
  10. Canad. Math. Bull. v.39 no.3 Conjugacy separability of certain polygonal products G. Kim https://doi.org/10.4153/CMB-1996-037-3
  11. Separability properties of certain tree products of groups G. Kim;C. Y. Tang
  12. Canad. Math. Bull. v.35 no.3 On the residual finiteness of polygonal products of nilpotent groups G. Kim;C. Y. Tang
  13. Pure and Applied Math. v.ⅩⅢ Combinatorial Group Theory W. Magnus;A. Karrass;D. Solitar
  14. Amer. Math. Soc. Transl. v.119 no.2 On homomorphisms onto finite groups A. I. Mal'cev
  15. Ivanov Gos.Ped. Inst. Ucen. Zap. Uchen. Zap. Karel. Ped. Inst. Ser. Fiz-Mat. Nauk v.18 Homomorphisms of finite groups A. I. Mal'cev
  16. Fund. Math. v.59 On the decidability of some problems in special classes of groups A. W. Mostowski
  17. J. Pure Appl. Algebra v.78 Separability properties of free groups and surface groups G. A. Niblo https://doi.org/10.1016/0022-4049(92)90019-C
  18. G. T. M. v.80 A course in the theory of groups D. J. S. Robinson
  19. J. London Math. Soc. v.17 Subgroups of surface groups are almost geometric P. Scott https://doi.org/10.1112/jlms/s2-17.3.555
  20. Trans. Amer. Math. Soc. v.156 Conjugacy separability of certain free products with amalyamation P. F. Stebe https://doi.org/10.2307/1995602