Here we consider two classes of torsion-free one-relator groups which have proved quite amenable to study-the cyclically pinched one-relator groups and the conjugacy pinched one-relator groups. The former is the class of groups which are free products of free groups with cyclic amalgamations while the latter is the class of HNN extensions of free groups with cyclic associated subgroups. Both are generalizations of surface groups. We compare and contrast results in these classes relative to n-freeness, separability properties including conjugacy separability, subgroup separability and residual finiteness, decision theoretic properties including the isomorphism problem and hyperbolicity.
@article{urn:eudml:doc:44269,
title = {Conjugacy pinched and cyclically pinched one-relator groups.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {207-227},
zbl = {0904.20019},
mrnumber = {MR1605642},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44269}
}
Fine, Benjamin; Rosenberger, Gerhard; Stille, Michael. Conjugacy pinched and cyclically pinched one-relator groups.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 207-227. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44269/