ON CERTAIN WEAK ENGEL-TYPE CONDITIONS IN GROUPS

被引：0

作者：

Meriano, Maurizio ^{[1
]}

Nicotera, Chiara ^{[1
]}

机构：

[1] Univ Salerno, Dipartimento Matemat, I-84100 Salerno, Italy

来源：

COMMUNICATIONS IN ALGEBRA | 2014年 / 42卷 / 10期

关键词：

Conjugate; Engel conditions; Solvable groups; Two-variable word; POINT-FREE PERMUTATIONS; TRANSITIVE GROUPS; FINITE-GROUPS; SUBGROUPS;

D O I：

10.1080/00927872.2013.806522

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let w(x, y) be a word in two variables and B the variety determined by w. In this paper we raise the following question: if for every pair of elements a, b in a group G there exists g is an element of G such that w(a(g) , b) = 1, under what conditions does the group G belong to B? In particular, we consider the n-Engel word w(x, y) = [x,(n) y]. We show that in this case the property is satisfied when the group G is metabelian. If n = 2, then we extend this result to the class of all solvable groups.

引用

页码：4241 / 4247

页数：7

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