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Tree products of cyclic subgroup separable groups. (English) Zbl 0886.20019

It is proved that certain finite tree products of cyclic subgroup separable groups are again cyclic subgroup separable. As consequences finite tree products of polycyclic-by-finite groups amalgamating central subgroups and finite tree products of finitely generated torsion-free nilpotent groups or free groups, amalgamating cyclic subgroups are cyclic subgroup separable. Another consequence is that many one-relator groups are cyclic subgroup separable.

MSC:

20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E26 Residual properties and generalizations; residually finite groups
20F05 Generators, relations, and presentations of groups
20F19 Generalizations of solvable and nilpotent groups
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