- Volume 48 Issue 3
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
- G. Baumslag,. Lecture notes on nilpotent groups, C. B. M. S. Regional Conf. Ser. in Math., Amer. Math. Soc. No. 2., (1971)
- D. Doniz. Residual properties of free products of infinitely many nilpotent groups amalgamating cycles, J. Algebra, 179(1996), 930-935. https://doi.org/10.1006/jabr.1996.0045
- K. W. Gruenberg. Residual properties of infinite soluble groups, Proc. London Math. Soc., (3), 7(1957), 29-62. https://doi.org/10.1112/plms/s3-7.1.29
- G. Higman. Amalgams of p-groups, J. Algebra, 1(1964), 301-305. https://doi.org/10.1016/0021-8693(64)90025-0
- G. Kim and J. McCarron. On amalgamated free products of residually p-finite groups, J. Algebra, 162(1)(1993), 1-11. https://doi.org/10.1006/jabr.1993.1237
- G. Kim and C. Y. Tang. On generalized free products of residually p-finite groups, J. Algebra, 201(1998), 317-327. https://doi.org/10.1006/jabr.1997.7256
- J. McCarron. Residual nilpotence and one relator groups, PhD thesis, University of Waterloo, Canada, (1995).
- P. C. Wong and C. K. Tang. Tree products of residually p-finite groups, Algebra Colloq., 2(3)(1995), 209-212.