Cyclically Presented Groups and Resultants

On the Structure of Some Deficiency Zero Groups

Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups

We study a class of Labelled Oriented Graph (LOG) group where the underlying graph is a tadpole graph. We show that such a group is the natural HNN extension of a cyclically presented group and investigate the relationship between the LOG group and the cyclically presented group. We relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented ...

Cyclically presented groups in which the relators involve at most three generators

Cyclically presented groups Gn(w) in which w involves at most three generators are studied. We classify when such groups have infinite abelianizations and apply this result to the groups Gn(x1x1+kx 1+`). As a further corollary we give sufficient conditions for the natural HNN extension of Gn(w) to be a high-dimensional knot group. By continuing Cavicchioli, Repovš, and Spaggiari’s investigation...

Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups

We study a classM of cyclically presented groups that includes both finite and infinite groups and is defined by a certain combinatorial condition on the defining relations. This class includes many finite metacyclic generalized Fibonacci groups that have been previously identified in the literature. By analysing their shift extensions we show that the groups in the class M are are coherent, su...

Largeness and Sq-Universality of cyclically Presented Groups

Largeness, SQ-universality, and the existence of free subgroups of rank 2 are measures of the complexity of a finitely presented group. We obtain conditions under which a cyclically presented group possesses one or more of these properties. We apply our results to a class of groups introduced by Prishchepov which contain, amongst others, the various generalizations of Fibonacci groups introduce...