Volume 6, Issue 1 (Vol. 6, No. 1 2020)                   mmr 2020, 6(1): 57-64 | Back to browse issues page

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Ramezan-Nassab M. Group Rings Satisfying Generalized Engel Conditions. mmr 2020; 6 (1) :57-64
URL: http://mmr.khu.ac.ir/article-1-2629-en.html
Kharazmi University , ramezann@khu.ac.ir
Abstract:   (1819 Views)

Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1)  y]=[[x ,_( n)  y]  , y]. In this paper we show that necessary and sufficient conditions for RG to satisfies [x^m(x,y)   ,_( n(x,y))  y]=0 is: 1) if r is a power of a prime p, then G is a locally nilpotent group and G' is a p-group, 2) if r=0 or r is not a power of a prime, then G is abelian. In this paper, also, we define some generalized Engel conditions on groups, then we present a result about unit group of group algebras which satisfies this kind of generalized Engel conditions. 

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Type of Study: Original Manuscript | Subject: alg
Received: 2017/05/31 | Revised: 2023/07/8 | Accepted: 2018/11/28 | Published: 2020/01/25 | ePublished: 2020/01/25

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