Building on previous results concerning hyperbolicity of groups Fibonacci type, we give an almost complete classification the (non-elementary) hyperbolic within this class. We are unable to determine status precisely two groups, namely Gilbert-Howie H ( 9 , 4 ) 7 . show that if is torsion-free then it not hyperbolic. consider class T(5) cyclically presented and classify Tits alternative holds.

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...