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On Biautomaticity of Non-Homogenous Small-Cancellation Groups

We define the notion of V(6) presentations that naturally generalize C(4)&T(4) and C(6) small-cancellation presentations. We consider V(6) groups (i.e. groups having V(6) presentations) where every piece is of length one. No natural geometrical interpretation is known for this class of groups. However, by using combinatorial and diagrammatical arguments, we construct a biautomatic structure for these groups.