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ON THE RESIDUAL FINITENESS OF CERTAIN POLYGONAL PRODUCTS OF FREE GROUPS

Kim, Goansu

  • Received : 2015.10.27
  • Published : 2016.07.31

Abstract

In general, polygonal products of free groups are not residually finite. Using the residual finiteness of polygonal products of nilpotent groups, we show that certain polygonal products of free groups are residually finite.

Keywords

polygonal products of groups;free groups;residually finite

References

  1. R. B. J. T. Allenby, The residual finiteness of polygonal products - Two counterexamples, Canad. Math. Bull. 37 (1994), no. 4, 433-436. https://doi.org/10.4153/CMB-1994-062-5
  2. R. B. J. T. Allenby, Polygonal products of polycyclic by finite groups, Bull. Austral. Math. Soc. 54 (1996), no. 3, 369-372. https://doi.org/10.1017/S0004972700021778
  3. R. B. J. T. Allenby and C. Y. Tang, On the residual finiteness of certain polygonal products, Canad. Math. Bull. 32 (1989), no. 1, 11-17. https://doi.org/10.4153/CMB-1989-002-8
  4. A. Karrass, A. Pietrowski and D. Solitar, The subgroups of polygonal products of groups, unpublished manuscript.
  5. G. Kim, On polygonal products of finitely generated abelian groups, Bull. Austral. Math. Soc. 45 (1992), no. 3, 453-462. https://doi.org/10.1017/S0004972700030343
  6. G. Kim, Cyclic subgroup separability of generalized free products, Canad. Math. Bull. 36 (1993), no. 3, 296-302. https://doi.org/10.4153/CMB-1993-042-7
  7. G. Kim, Conjugacy separability of certain polygonal products, Canad. Math. Bull. 39 (1996), no. 3, 294-307. https://doi.org/10.4153/CMB-1996-037-3
  8. G. Kim and C. Y. Tang, On the residual finiteness of polygonal products of nilpotent groups, Canad. Math. Bull. 35 (1992), no. 3, 390-399. https://doi.org/10.4153/CMB-1992-052-8
  9. W. Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen ring, Math. Ann. 111 (1935), 259-280. https://doi.org/10.1007/BF01472217
  10. W. Magnus, Residually finite groups, Bull. Amer. Math. Soc. 75 (1969), 305-316. https://doi.org/10.1090/S0002-9904-1969-12149-X
  11. A. W. Mostowski, On the decidability of some problems in special classes of groups, Fund. Math. 59 (1966), 123-135. https://doi.org/10.4064/fm-59-2-123-135
  12. D. J. S. Robinson, A course in the theory of groups, G. T. M. 80. Springer-Verlag, New York-Heidelberg-Berlin, 1982.
  13. J. S. Rose, A Course on Group Theory, Dover Publ., New York, 1994.