On the Exponent of Triple Tensor Product of p-Groups

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HADIZADEH H.; JAFARI S.H.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2020 | Volume:5 | Issue:22 Page(s): 77-83

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Title

On the Exponent of Triple Tensor Product of p-Groups

Author(s)

HADIZADEH H. | JAFARI S.H. | Issue Writer Certificate

Keywords

Non-abelian tensor product

nilpotent group

nilpotency class

exponent of group

Abstract

The Non-abelian tensor product of groups which has its origins in algebraic K-theory as well as in homotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of Non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, computation of c-fold tensor products is generally a difficult problem. Several authors have given upper bounds for the order of G, when G is a finite p-group. In this paper we determine a bound for the exponent triple tensor product which sharpens a bound of G. Ellis. Let G be a nilpotent group of nilpotency class k≥ 3 and prime power exponent P^e (where p is a prime and is not equal 3). In this paper, we show that the exponent of triple tensor product of G, that is, (G⨂ G)⨂ G, divides P^([k/2]-1)e where [k/2] denotes the smallest integer n such that n≥ k/2. In this way, the exponent provided by Ellis is improved.

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APA: Copy

HADIZADEH, H., & JAFARI, S.H.. (2020). On the Exponent of Triple Tensor Product of p-Groups. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(22 ), 77-83. SID. https://sid.ir/paper/952087/en

Vancouver: Copy

HADIZADEH H., JAFARI S.H.. On the Exponent of Triple Tensor Product of p-Groups. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;5(22 ):77-83. Available from: https://sid.ir/paper/952087/en

IEEE: Copy

H. HADIZADEH, and S.H. JAFARI, “On the Exponent of Triple Tensor Product of p-Groups,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 22 , pp. 77–83, 2020, [Online]. Available: https://sid.ir/paper/952087/en

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