Non-abelian tensor analogues of 2-auto Engel groups
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1097-1105
Printed July 31, 2015
Mohammad Reza R. Moghaddam and Mohammad Javad Sadeghifard
Islamic Azad University, Islamic Azad University
Abstract : \noindent The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe \cite{dp} and Moravec \cite{pm}. Using the automorphisms of a given group $G$, we introduce the notion of tensor analogue of 2-auto Engel elements in $G$ and investigate their properties. Also the concept of $2_{\otimes}$-auto Engel groups is introduced and we prove that if $G$ is a $2_{\otimes}$-auto Engel group, then $G\otimes {\rm Aut}(G)$ is abelian. Finally, we construct a non-abelian $2$-auto-Engel group $G$ so that its non-abelian tensor product by ${\rm Aut}(G)$ is abelian.
Keywords : non-abelian tensor product, auto-Engel element, autocommutator subgroup, absolute centre
MSC numbers : Primary 20F28, 20F45; Secondary 20F99
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