Engel elements in some fractal groups
نویسندگان
چکیده
منابع مشابه
un 2 00 4 Notes on Engel groups and Engel elements in groups . Some generalizations
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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Let nand k be positive integers. We say that a group G satisfies the condition £(n) (respectively, £dn)) if and only if any set with n + 1 elements of G contains two distinct elements x, y such that [x,t y] = 1 for some positive integer t = t(x, y) (respectively, [X,k y] = 1). Here we study certain groups satisfying these conditions. We prove that if G is a finite group satisfying the condition...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2018
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-018-1218-3