Right 4-Engel elements of a group

2010/01/23 by A. Abdollahi, Abdollahi, A., H. Khosravi +1
Mathematics · #20D45 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20D45

paper · pdf · doi:10.48550/arxiv.1001.4156

to appear in Journal of Algebra and its Applications; This paper has some overlaps with arXiv:0906.2439, however the proofs are clearer and arXiv:0906.2439 will not publish anywhere

arxiv created 2010/01/23 · arxiv updated 2010/02/26

Abstract

We prove that the set of right 4-Engel elements of a group G is a subgroup for locally nilpotent groups G without elements of orders 2, 3 or 5; and in this case the normal closure <x>^G is nilpotent of class at most 7 for each right 4-Engel elements x of G.

Citations

• When right n-Engel elements of a group form a subgroup?

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