Generalized Triangle Groups of Type (2, 3, 2) with No Cyclic Essential Representations

A conjecture of Rosenberger asserts that every generalized triangle group either is virtually soluble or contains a nonabelian free subgroup. Modulo two exceptional cases, we verify this conjecture for generalized triangle groups of type (2, 3, 2) which do not admit essential representations onto the cyclic group of order 6.