منابع مشابه
On the Right and Left 4-engel Elements
In this paper we study left and right 4-Engel elements of a group. In particular, we prove that 〈a, a〉 is nilpotent of class at most 4, whenever a is any element and b are right 4-Engel elements or a are left 4-Engel elements and b is an arbitrary element of G. Furthermore we prove that for any prime p and any element a of finite p-power order in a group G such that a ∈ L4(G), a, if p = 2, and ...
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in this paper we study right $n$-engel group elements. by modifying a group constructed by newman and nickel, we construct, for each integer $ngeq 5$, a 2-generator group $g =langle a, brangle$ with the property that $b$ is a right $n$-engel element but where $[b^k,_n a]$ is of infinite order when $knotin {0, 1}$.
متن کاملLeft 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.
متن کاملun 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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Multiple criteria decision making (MCDM) problem is one of the famous different kinds of decision making problems. In more cases in real situations, determining the exact values for MCDM problems is difficult or impossible. So, the values of alternatives with respect to the criteria or / and the values of criteria weights, are considered as fuzzy values (fuzzy numbers). In such conditions, th...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2010
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870902887112