On the structure of right 3-Engel subgroups

Peter G Crosby

doi:10.1016/j.jalgebra.2011.12.031

On the structure of right 3-Engel subgroups

Peter G Crosby

Department of Mathematical Sciences

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Abstract

We state and prove two sharp results on the structure of normal subgroups consisting of right 3-Engel elements. First we prove that if H is a 3-torsion-free such subgroup of a group G and x ∈ G, then [H, 4〈 x 〉 G] = {1}. When H is additionally {2, 5}-torsion-free, we prove that [H, 8G] = {1}.

Original language	English
Pages (from-to)	205-220
Number of pages	16
Journal	Journal of Algebra
Volume	365
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.12.031
Publication status	Published - Apr 2012

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NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, vol 355, issue 1, DOI 10.1016/j.jalgebra.2011.12.031
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title = "On the structure of right 3-Engel subgroups",

abstract = "We state and prove two sharp results on the structure of normal subgroups consisting of right 3-Engel elements. First we prove that if H is a 3-torsion-free such subgroup of a group G and x ∈ G, then [H, 4〈 x 〉 G] = \{1\}. When H is additionally \{2, 5\}-torsion-free, we prove that [H, 8G] = \{1\}.",

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AB - We state and prove two sharp results on the structure of normal subgroups consisting of right 3-Engel elements. First we prove that if H is a 3-torsion-free such subgroup of a group G and x ∈ G, then [H, 4〈 x 〉 G] = {1}. When H is additionally {2, 5}-torsion-free, we prove that [H, 8G] = {1}.

UR - https://www.scopus.com/pages/publications/84857033521

UR - http://dx.doi.org/10.1016/j.jalgebra.2011.12.031

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On the structure of right 3-Engel subgroups

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