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Categorizing finite $p$ -groups by the order of their non-abelian tensor squares

S. Hadi Jafari

Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

E-mail Address: s.hadijafari@mshdiau.ac.ir

https://doi.org/10.1142/S021949881650095XCited by:5 (Source: Crossref)

Abstract

Let $G$ be a non-abelian $d$ -generator finite $p$ -group of order $p^{n}$ . Ellis and McDermott in 1996 proved that $| G \otimes G | \leq p^{n d}$ . In the present paper, we improve this upper bound and show that $| G \otimes G | \leq p^{(n - 1) d + 2}$ . Also the $p$ -groups with derived subgroup of order $p$ which attain the bound are obtained. Among other results, we classify all finite $p$ -groups of order $p^{n}$ , for $n \leq 7$ , with $| G \otimes G | = p^{n m - 1}$ , where $| G^{a b} | = p^{m}$ .

Communicated by S. Sidki

Keywords:

AMSC: 20D15, 20J06

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