Geodesic
Cyclic Subgroup Separability of Generalized Free Products
Canadian mathematical bulletin, Tome 36 (1993) no. 3, pp. 296-302

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

We derive a criterion for a generalized free product of groups to be cyclic subgroup separable. We see that most of the known results for cyclic subgroup separability are covered by this criterion, and we apply the criterion to polygonal products of groups. We show that a polygonal product of finitely generated abelian groups, amalgamating cyclic subgroups, is cyclic subgroup separable.
DOI : 10.4153/CMB-1993-042-7
Mots-clés : 20E26, 20E06, generalized free products, polygonal products, residually finite, cyclic subgroup separable (πc). 
Kim, Goansu. Cyclic Subgroup Separability of Generalized Free Products. Canadian mathematical bulletin, Tome 36 (1993) no. 3, pp. 296-302. doi: 10.4153/CMB-1993-042-7
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[1] 1. Allenby, R. B. J. T. and Gregorac, R. J., On locally extended residually finite groups. In: Lecture Notes in Mathematics 319, 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. Allenby, R. B. J. T. and Tang, C. Y., The residual finitene s s of some one-relator groups with torsion, J. Algebra (1) 71(1981), 132— 140. Google Scholar

[4] 4. Baumslag, G., On the residual finiteness of generalized free products of nilpotent groups, Trans. Amer. Math. Soc. 106(1963), 193–209 Google Scholar

[5] 5. Boler, J. and Evans, B., The free product of re sidually finite groups amalgamated along retracts is residually finite, Proc. Amer. Math. Soc.6(1973), 284–285. Google Scholar

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

[7] 7. Evans, B., Cyclic amalgamations of residually finite groups, Pacific J. Math. 55(1974), 371–379. Google Scholar

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

[9] 9. Higman, G., A finitely related group with an isomorphic proper factor group, J. London Math. Soc. 26(1951), 59–61. Google Scholar

[10] 10. Kim, G., Conjugacy and Subgroup Separability of Generalized Free Product, Ph.D. thesis submitted to University of Waterloo, 1991. Google Scholar

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

[12] 12. Lipschutz, S., Groups with solvable conjugacy problems, Illinois J. Math. 24(1980), 192–195. Google Scholar

[13] 13. Shirvani, M., A converse to a residual finitene s s theorem of G. Baumslag, Proc. Amer. Math. Soc. (3) 104(1988), 703–706. Google Scholar

[14] 14. Wehrfritz, B. A. F., The residual finitene s s of some generalized free products, J. London Math. Soc. (2) 24(1981), 123–126. Google Scholar

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