On the Residual Finiteness of Certain Polygonal Products
Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 11-17

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We give examples to show that unlike generalized free products of groups (g.f.p.) polygonal products of finitely generated (f.g.) nilpotent groups with cyclic amalgamations need not be residually finite (R ) and polygonal products of finite p-groups with cyclic amalgamations need not be residually nilpotent. However, polygonal products f.g. abelian groups are R , and under certain conditions polygonal products of finite p-groups with cyclic amalgamations are R .
DOI : 10.4153/CMB-1989-002-8
Mots-clés : 20E06, 20E26, 20F18, 20F05
Allenby, R. B. J. T.; Tang, C. Y. On the Residual Finiteness of Certain Polygonal Products. Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 11-17. doi: 10.4153/CMB-1989-002-8
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[1] 1. Baumslag, G., on the residual finit eness of generalized free products of nilpotent groups, Trans. Amer. Math. Soc. 106 (1963), pp. 193–209. Google Scholar

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

[3] 3. Burns, R. G., A note on free groups, Proc. Amer. Math. Soc. 23 (1969), pp. 14–17. Google Scholar

[4] 4. Hall, M., Jr., Coset representations in free groups, Trans. Amer. Math. Soc, 67 (1949), pp. 421–432. Google Scholar

[5] 5. Higman, G., Amalgam of p-groups, J. of Algebra 1 (1964), pp. 301–305. Google Scholar

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 Karrass, A., Pietrowski, A. and Solitar, D., The subgroups of polygonal products of groups, unpublished manuscript.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

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

[8] 8. Neumann, B. H. and H. Neumann, A contribution to the embedding theory of group amalgams, Proc. London Math. Soc. (3) 3 (1953), pp. 243–256. Google Scholar

[9] 9. Wiegold, J., Nilpotent products of groups with amalgamations, Publ. Math. Debrecen 6 (1959), pp. 131–168. Google Scholar

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