Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator

Abstract

A group obtained from a nontrivial group by adding one generator and one relator which is a proper power of a word in which the exponent-sum of the additional generator is one contains the free square of the initial group and almost always (with one obvious exception) contains a non-abelian free subgroup. If the initial group is involution-free or the relator is at least third power, then the obtained group is SQ-universal and relatively hyperbolic with respect to the initial group.

11 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V3: revised following referee's comments

References in corpus (6)

• The conjugacy problem for relatively hyperbolic groups
• How to generalize known results on equations over groups
• Free subgroups of one-relator relative presentations
• The Kervaire-Laudenbach conjecture and presentations of simple groups
• The SQ-universality of one-relator relative presentations
• The structure of one-relator relative presentations and their centres

Cited by in corpus (5)

• Quasiperiodic and mixed commutator factorizations in free products of groups
• Equations over solvable groups
• Commutator length of powers in free products of groups
• Commutators cannot be proper powers in metric small-cancellation torsion-free groups
• Malnormality and centers in one-relator relative presentations