Conjugacy Separability of Certain Polygonal Products
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 294-307

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

We show that polygonal products of polycyclic-by-finite groups amalgamating central cyclic subgroups, with trivial intersections, are conjugacy separable. Thus polygonal products of finitely generated abelian groups amalgamating cyclic subgroups, with trivial intersections, are conjugacy separable. As a corollary of this, we obtain that the group A 1 *〈a1〉A 2 *〈a2〉 • • • *〈a m-1〉Am is conjugacy separable for the abelian groups Ai .
DOI : 10.4153/CMB-1996-037-3
Mots-clés : Primary: 20E26, 20E06, secondary: 20F10, Polygonal products, generalized free products, conjugacy separable, residuallyfinite
Kim, Goansu. Conjugacy Separability of Certain Polygonal Products. Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 294-307. doi: 10.4153/CMB-1996-037-3
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[1] 1. Allenby, R. B. J. T. and Tang, C. Y, On the residual finiteness of certain polygonal products, Canad. Math. Bull. (1)32(1989), 11–17. Google Scholar

[2] 2. Dyer, J. L., Separating conjugates in free-by-finite groups, J. London Math. Soc. (2) 20( 1979), 215–221. Google Scholar

[3] 3. Dyer, J. L., Separating conjugates in amalgamated free products and HNN extensions, J. Austral. Math. Soc. Ser. A ( 1 ) 29( 1980), 35–51. Google Scholar

[4] 4. Fine, B. and Rosenberger, G., Conjugacy separability of Fuchsian groups and related questions, Contemp. Math., Amer. Math. Soc. 109(1990), 11–18. Google Scholar

[5] 5. Formanek, E., Conjugate separability in polycyclic groups, J. Algebra 42( 1976), 1—10. Google Scholar

[6] 6. Green, E. R., Graph Products of Groups, Ph. D. thesis, University of Leeds, 1990. Google Scholar

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 Karrass, A., Pietrowski, A., and Solitar, D., The subgroups of polygonal products of groups, unpublished manuscript.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

[8] 8. Kim, G., Conjugacy separability of certain free product amalgamating retracts, preprint. Google Scholar

[9] 9. Kim, G., On polygonal products of finitely generated abelian groups, Bull. Austral. Math. Soc. (3) 45(1992), 453–462. Google Scholar

[10] 10. Kim, G., Cyclic subgroup separability of generalized free products, Canad. Math. Bull. (3) 36(1993), 296–302. Google Scholar

[11] 11. Kim, G., McCarron, J., and C. Y Tang, Adjoining roots to conjugacy separable groups, J. Algebra 176(1995), 327–345. Google Scholar

[12] 12. Kim, G. and C. Y Tang, On the residual finiteness of polygonal products of nilpotent groups, Canad. Math. Bull. (3)35(1992), 390–399. Google Scholar

[13] 13. Kim, G. and Tang, C. Y, Polygonal products which are residually finite p-groups. In: Group Theory Proc. of the Biennial Ohio State-Dennison Conference, World Sci. Pub. Co., Singapore, 1993, 275—287. Google Scholar

[14] 14. Magnus, W., Karrass, A., and Solitar, D., Combinatorial Group Theory, Pure and Applied Math. Vol. XIII, Wiley-Interscience, New York, London, Sydney, 1966. Google Scholar

[15] 15. Tang, C. Y., Conjugacy separability of generalized free products of surface groups, J. Pure Appl. Algebra, to appear. Google Scholar

[16] 16. Tang, C. Y., Conjugacy separability of generalized free products of certain conjugacy separable groups, Canad. Math. Bull. 38(1995), 120–127. Google Scholar

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