Groups of prime power order and their nonabelian tensor squares |
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Authors: | Primož Moravec |
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Affiliation: | 1.Department of Mathematics,University of Ljubljana,Ljubljana,Slovenia |
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Abstract: | We prove that the nonabelian tensor square of a powerful p-group is again a powerful p-group. Furthermore, If G is powerful, then the exponent of G ⊕ G divides the exponent of G. New bounds for the exponent, rank, and order of various homological functors of a given finite p-group are obtained. In particular, we improve the bound for the order of the Schur multiplier of a given finite p-group obtained by Lubotzky and Mann. |
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