We use results concerning the Smith forms of circulant matrices to identify when cyclically presented groups have free abelianisation and so can be Labelled Oriented Graph (LOG) groups. generalize a theorem Odoni Cremona show that for fixed defining word, whose corresponding representer polynomial has an irreducible factor is not cyclotomic equal ±t, there are at most finitely many n which n-ge...

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 ...

‎‎in cite{fr 1‎, ‎fr 2} using faithful complex representations of cyclically pinched and conjugacy pinched one-relator groups we proved that any limit group has a faithful representation in $psl(2,c)$‎. ‎further this representation can be effectively constructed using the jsj decomposition‎. ‎in this note we show that any hyperbolic cyclically pinched one-relator group with maximal amalgamated ...