On the third tensor power of a nilpotent group of class two

Let G be a nilpotent group of class two and G ⊗ G be its nonabelian tensor square. In this paper, we determine an upper bound for d ( ( G ⊗ G ) ⊗ G ) in terms of d ( G ), where d ( G ) is the minimal number of generators of G . In particular, we show that the bound is attained if G is a finitely gen...

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Bibliographic Details
Published in:	Proceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 131; no. 2
Main Authors:	ASHEGHI, E, JAFARI, S HADI
Format:	Journal Article
Language:	English
Published:	New Delhi Springer India 01-10-2021 Springer Nature B.V
Subjects:	Mathematical analysis Mathematics Mathematics and Statistics Tensors Upper bounds nilpotent group Secondary: 20D15 Nonabelian tensor product Primary: 19C09 minimal number of generators
Online Access:	Get full text
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Summary:	Let G be a nilpotent group of class two and G ⊗ G be its nonabelian tensor square. In this paper, we determine an upper bound for d ( ( G ⊗ G ) ⊗ G ) in terms of d ( G ), where d ( G ) is the minimal number of generators of G . In particular, we show that the bound is attained if G is a finitely generated free nilpotent group of class two.
ISSN:	0253-4142 0973-7685
DOI:	10.1007/s12044-021-00629-4