Several authors, including Lyndon--Schupp (1997), take another convention when some relator is a proper power, in order to avoid this multiplicity. This sometimes leads to contradictions in their exposition, such as in Prop. III.4.3 of Lyndon--Schupp. With the convention used here, the Cayley complex is the universal covering of the -skeleton of the standard classifying space associated with the presentation.

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