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OUTER AUTOMORPHISM GROUPS OF POLYGONAL PRODUCTS OF CERTAIN CONJUGACY SEPARABLE GROUPS

  • Kim, Goan-Su (DEPARTMENT OF MATHEMATICS YEUNGNAM UNIVERSITY) ;
  • Tang, Chi Yu (DEPARTMENT OF PURE MATHEMATICS UNIVERSITY OF WATERLOO)
  • Published : 2008.11.01

Abstract

Grossman [7] showed that certain cyclically pinched 1-relator groups have residually finite outer automorphism groups. In this paper we prove that tree products of finitely generated free groups amalgamating maximal cyclic subgroups have residually finite outer automorphism groups. We also prove that polygonal products of finitely generated central subgroup separable groups amalgamating trivial intersecting central subgroups have residually finite outer automorphism groups.

Keywords

References

  1. R. B. J. T. Allenby, G. Kim, and C. Y. Tang, Outer automorphism groups of certain orientable Seifert 3-manifold groups, Combinatorial group theory, discrete groups, and number theory, 15-22, Contemp. Math., 421, Amer. Math. Soc., Providence, RI, 2006 https://doi.org/10.1090/conm/421/08022
  2. R. B. J. T. Allenby, Outer automorphism groups of non-orientable Seifert 3-manifold groups, Preprint
  3. R. B. J. T. Allenby, Residual finiteness of outer automorphism groups of certain pinched 1-relator groups, J. Algebra 246 (2001), no. 2, 849-858 https://doi.org/10.1006/jabr.2001.8987
  4. R. B. J. T. Allenby, Residual finiteness of outer automorphism groups of finitely generated nontriangle Fuchsian groups, Internat. J. Algebra Comput. 15 (2005), no. 1, 59-72 https://doi.org/10.1142/S0218196705002104
  5. G. Baumslag, Automorphism groups of residually finite groups, J. London Math. Soc. 38 (1963), 117-118 https://doi.org/10.1112/jlms/s1-38.1.117
  6. B. Fine and G. Rosenberger, Conjugacy separability of Fuchsian groups and related questions, Combinatorial group theory (College Park, MD, 1988), 11-18, Contemp. Math., 109, Amer. Math. Soc., Providence, RI, 1990 https://doi.org/10.1090/conm/109/1076372
  7. E. K. Grossman, On the residual finiteness of certain mapping class groups, J. London Math. Soc. (2) 9 (1974/75), 160-164 https://doi.org/10.1112/jlms/s2-9.1.160
  8. G. Kim, Outer automorphism groups of certain polygonal products of groups, Bull. Korean Math. Soc. 45 (2008), no. 1, 45-52 https://doi.org/10.4134/BKMS.2008.45.1.045
  9. G. Kim and C. Y. Tang, Separability properties of certain polygonal products of groups, J. Korean Math. Soc. 39 (2002), no. 3, 461-494 https://doi.org/10.4134/JKMS.2002.39.3.461
  10. G. Kim, Separability properties of certain tree products of groups, J. Algebra 251 (2002), no. 1, 323-349 https://doi.org/10.1006/jabr.2001.9134
  11. W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney 1966
  12. L. Ribes, D. Segal, and P. A. Zalesskii, Conjugacy separability and free products of groups with cyclic amalgamation, J. London Math. Soc. (2) 57 (1998), no. 3, 609-628 https://doi.org/10.1112/S0024610798006267
  13. B. A. F. Wehrfritz, Two remarks on polycyclic groups, Bull. London Math. Soc. 26 (1994), no. 6, 543-548 https://doi.org/10.1112/blms/26.6.543
  14. D. Wise, A residually finite version of Rips's construction, Bull. London Math. Soc. 35 (2003), no. 1, 23-29 https://doi.org/10.1112/S0024609302001406

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  3. Conjugacy separability and outer automorphism groups of certain HNN extensions vol.334, pp.1, 2011, https://doi.org/10.1016/j.jalgebra.2011.02.038
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