The exponent of the non‐abelian tensor square and related constructions ofp‐groups

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AbstractLetGbe a finitep‐group. In this paper we obtain bounds for the exponent of the non‐abelian tensor square and a certain extension of by . In particular, we bound in terms of and whenGadmits some specific normal subgroupN. We also establish bounds for in terms of and either the nilpotency class or the coclass of the groupG, improving some existing bounds.