SQ-universality of one-relator relative presentations. (English. Russian original) Zbl 1188.20024
Sb. Math. 197, No. 10, 1489-1508 (2006); translation from Mat. Sb. 197, No. 10, 87-108 (2006).
Summary: Adding two generators and an arbitrary relator to a non-trivial torsion-free group one always obtains an SQ-universal group. In the course of the proof of this theorem one obtains several other results of independent interest. For instance, the addition of a generator and one relator in which the sum of the exponents of the additional generator is equal to 1 to a free product of two non-trivial torsion-free groups also produces an SQ-universal group.
MSC:
| 20F05 | Generators, relations, and presentations of groups |
| 20E06 | Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations |
| 20E26 | Residual properties and generalizations; residually finite groups |
| 20E07 | Subgroup theorems; subgroup growth |
| 20F06 | Cancellation theory of groups; application of van Kampen diagrams |
