Left $3$-Engel elements of odd order in groups
نویسندگان
چکیده
منابع مشابه
Left 3-engel Elements in Groups
In this paper we study left 3-Engel elements in groups. In particular, we prove that for any prime p and any left 3-Engel element x of finite p-power order in a group G, x is in the Baer radical of G. Also it is proved that 〈x, y〉 is nilpotent of class 4 for every two left 3-Engel elements in a group G.
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Engel groups and Engel elements became popular in 50s. We consider in the paper the more general nil-groups and nil-elements in groups. All these notions are related to nilpotent groups and nilpo-tent radicals in groups. These notions generate problems which are parallel to Burnside problems for periodic groups. The first three theorems of the paper are devoted to nil-groups and Engel groups, w...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2019
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14389