Some new properties of non-abelian tensor analogues of 2-auto Engel groups

Author(s):

Mostafa Sajedi , Hamid Darabi *

Message:
Article Type:
Research/Original Article (بدون رتبه معتبر)
Abstract:
In this paper, we study the concept of $2_{\otimes}$-auto Engel groups. Among other results, we prove that for any group $G$, if every element of $G\otimes Aut(G)$ is $2_{\otimes}$-Engel group, then $\left<(g\otimes\alpha),(g\otimes\alpha)^{g^{\prime}\otimes\alpha^{\prime}}\right>$ is a nilpotent subgroup of class at most $2$ in $G\otimes Aut(G)$, for all $g,g^{\prime} \in G$ and $\alpha ,\alpha^{\prime}\in Aut(G)$.
Keywords:

Non-abelian tensor product , auto Engel element , autocommutator subgroup

Language:
English
Published:
Caspian Journal of Mathematical Sciences, Volume:12 Issue: 1, Winter Spring 2023
Pages:
204 to 210
https://www.magiran.com/p2695628  
سامانه نویسندگان
  • Author (1)
    Mostafa Sajedi
    Sajedi، Mostafa
  • Corresponding Author (2)
    Hamid Darabi
    Assistant Professor Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran,
    Darabi، Hamid
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