Group Rings Satisfying Generalized Engel Conditions

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Ramezan Nassab Mojtaba

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Journal: MATHEMATICAL RESEARCHES Year:2020 | Volume:6 | Issue:1 Page(s): 57-64

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Information Journal Paper

Title

Group Rings Satisfying Generalized Engel Conditions

Author(s)

Ramezan Nassab Mojtaba | Issue Writer Certificate

Keywords

Group ringsQ1

Engel groupsQ1

Generalized Lie Engel ringsQ1

Abstract

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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APA: Copy

Ramezan Nassab, Mojtaba. (2020). Group Rings Satisfying Generalized Engel Conditions. MATHEMATICAL RESEARCHES, 6(1 ), 57-64. SID. https://sid.ir/paper/386970/en

Vancouver: Copy

Ramezan Nassab Mojtaba. Group Rings Satisfying Generalized Engel Conditions. MATHEMATICAL RESEARCHES[Internet]. 2020;6(1 ):57-64. Available from: https://sid.ir/paper/386970/en

IEEE: Copy

Mojtaba Ramezan Nassab, “Group Rings Satisfying Generalized Engel Conditions,” MATHEMATICAL RESEARCHES, vol. 6, no. 1 , pp. 57–64, 2020, [Online]. Available: https://sid.ir/paper/386970/en

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