Residual P-Finiteness of Certain Generalized Free Products of Nilpotent Groups

Kim, Goan-Su;Lee, Young-Mi;McCarron, James

  • Received : 2008.01.22
  • Published : 2008.09.30


We show that free products of finitely generated and residually p-finite nilpotent groups, amalgamating p-closed central subgroups are residually p-finite. As a consequence, we are able to show that generalized free products of residually p-finite abelian groups are residually p-finite if the amalgamated subgroup is closed in the pro-p topology on each of the factors.


generalized free products;residually finite p-groups;p-closed subgroups;p-filters


  1. G. Baumslag,. Lecture notes on nilpotent groups, C. B. M. S. Regional Conf. Ser. in Math., Amer. Math. Soc. No. 2., (1971)
  2. D. Doniz. Residual properties of free products of infinitely many nilpotent groups amalgamating cycles, J. Algebra, 179(1996), 930-935.
  3. K. W. Gruenberg. Residual properties of infinite soluble groups, Proc. London Math. Soc., (3), 7(1957), 29-62.
  4. G. Higman. Amalgams of p-groups, J. Algebra, 1(1964), 301-305.
  5. G. Kim and J. McCarron. On amalgamated free products of residually p-finite groups, J. Algebra, 162(1)(1993), 1-11.
  6. G. Kim and C. Y. Tang. On generalized free products of residually p-finite groups, J. Algebra, 201(1998), 317-327.
  7. J. McCarron. Residual nilpotence and one relator groups, PhD thesis, University of Waterloo, Canada, (1995).
  8. P. C. Wong and C. K. Tang. Tree products of residually p-finite groups, Algebra Colloq., 2(3)(1995), 209-212.