Abstract
In this paper, we study some properties of the non-abelian tensor product of two groups G and H. More precisely, if G is abelian and H is a nilpotent group, then an upper bound for the exponent of G ⊗ H is obtained. Using our results, we obtain some upper bounds for the exponent of the Schur multiplier of the non-abelian tensor product of groups. Finally, an abelian group is constructed by taking non-abelian tensor product of groups.
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