Geodesic
On the Residual Finiteness of Polygonal Products of Nilpotent Groups
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 390-399

Voir la notice de l'article provenant de la source Cambridge University Press

In general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.
DOI : 10.4153/CMB-1992-052-8
Mots-clés : 20E06, 20E26, 20F18, 20D40, 20F05, Generalized free products, polygonal products, nilpotent groups, isolated subgroups, subgroup separability 
Kim, Goansu; Tang, C. Y. On the Residual Finiteness of Polygonal Products of Nilpotent Groups. Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 390-399. doi: 10.4153/CMB-1992-052-8
@article{10_4153_CMB_1992_052_8,
     author = {Kim, Goansu and Tang, C. Y.},
     title = {On the {Residual} {Finiteness} of {Polygonal} {Products} of {Nilpotent} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {390--399},
     year = {1992},
     volume = {35},
     number = {3},
     doi = {10.4153/CMB-1992-052-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-052-8/}
}
TY  - JOUR
AU  - Kim, Goansu
AU  - Tang, C. Y.
TI  - On the Residual Finiteness of Polygonal Products of Nilpotent Groups
JO  - Canadian mathematical bulletin
PY  - 1992
SP  - 390
EP  - 399
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-052-8/
DO  - 10.4153/CMB-1992-052-8
ID  - 10_4153_CMB_1992_052_8
ER  - 
%0 Journal Article
%A Kim, Goansu
%A Tang, C. Y.
%T On the Residual Finiteness of Polygonal Products of Nilpotent Groups
%J Canadian mathematical bulletin
%D 1992
%P 390-399
%V 35
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-052-8/
%R 10.4153/CMB-1992-052-8
%F 10_4153_CMB_1992_052_8

[1] 1. Allenby, R. B. J. T. and Gregorac, R. J., On locally extended residually finite groups , Lecture notes in Math. Springer Verlag, New York, (1973), 9–17. Google Scholar

[2] 2. Allenby, R. B. J. T. and Tang, C. Y., On the residual finitene s s of certain polygonal products, Canad. Math. Bull. (1)32(1989), 11–17. Google Scholar

[3] 3. Baumslag, G., Lecture notes on nilpotent groups , Amer. Math. Soc, C.B.M.S. Regional Conf. Ser. in Math. 2, 1971. Google Scholar

[4] 4. Brunner, A. M., Frame, M. L., Lee, Y. W. and Wielenberg, N. J., Classifying the torsion-free subgroups of the Picard group, Trans. Amer. Math. Soc. 282(1984), 205–235. Google Scholar

[5] 5. Boler, J. and Evans, B., The free product of residually finite groups amalgamated along retracts is residually finite, Proc. Amer. Math. Soc. 37(1973), 50–52. Google Scholar

[6] 6. Fine, B., Algebraic theory of the Bianchi groups , Marcel Dekker Inc., New York, 1989. Google Scholar

[7] 7. Higman, G., A remark on finitely generated nilpotent groups, Proc. Amer. Math. Soc. 6(1955), 284–285. Google Scholar

[8] 8. Karrass, A., Pietrowski, A. and Solitar, D., The subgroups of polygonal products of groups, unpublished manuscript. Google Scholar

[9] 9. Neumann, B. H., An essay on free products ofgroups with amalgamations, Philos. Trans. Roy. Soc. London, (A) 246(1954), 503–554. Google Scholar

Cité par Sources :