On the Right and Left 4-Engel Elements
On the Right and Left 4-Engel Elements
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论左右4恩格尔要素
DOI：
10.1080/00927870902887112
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发表时间：
2009
影响因子：
0.7
通讯作者：
H. Khosravi
中科院分区：
文献类型：
--
作者：
A. Abdollahi;H. Khosravi
本文研究了群的左、右4-Engel元。特别地，当a为有限阶且B ±1为右4-Engel元或a ±1为左4-Engel元且B为G的任意元时，证明了G a，a B ≤ 4类幂零.进一步证明了对群G中的任意素数p和任意有限p-幂阶元a，使得a ±1 ∈ L4（G），a4（若p = 2）和ap（若p为奇素数）在G的Baer根中.
In this article we study left and right 4-Engel elements of a group. In particular, we prove that ⟨a, a b ⟩ is nilpotent of class at most 4, whenever a is of finite order and b ±1 are right 4-Engel elements or a ±1 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 ±1 ∈ L 4(G), a 4, if p = 2, and a p , if p is an odd prime number, is in the Baer radical of G.