On the Right and Left 4-engel Elements
نویسنده
چکیده
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 a, if p is an odd prime number, is in the Baer radical of G.
منابع مشابه
Results on Engel Fuzzy Subgroups
In the classical group theory there is an open question: Is every torsion free n-Engel group (for n ≥ 4), nilpotent?. To answer the question, Traustason [11] showed that with some additional conditions all 4-Engel groups are locally nilpotent. Here, we gave some partial answer to this question on Engel fuzzy subgroups. We show that if μ is a normal 4-Engel fuzzy subgroup of ...
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