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A conjecture of Roseberger asserts that every generalised triangle groupeither is virtually soluble or contains a non-abelian free subgroup. Modulo twoexceptional cases, we verify this conjecture for generalised triangle groups oftype (2,3,2) which do not admit essential representations onto the cyclic groupof order 6.

Generalised triangle groups of type (2,3,2) with no cyclic essential representations