The concept of tensor analogues of right 2-Engel elements in groups were defined and
studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group …

The third author et al. in 2013, introduced and studied the concept of auto-Bell groups. A
group G is said to be n-auto-Bell if [x< sup> n, α]=[x, α< sup> n], for all x in G, α in Aut (G) and …

Let x be an element of a group G and α be an automorphism of G. Then for a positive integer
n, the autocommutator [x, n α] is defined inductively by [x, α]= x− 1xα= x− 1α (x) and [x, n+ 1 …

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 …

The relative Cayley graph of a group G with respect to its proper subgroup H, is a graph
whose vertices are elements of G and two vertices h∈ H and g∈ G are adjacent if g= hc for …

The notion of 2_ ⊗ 2⊗-auto Engel subgroups was studied in Moghaddam and Sadeghifard
(Bull Korean Math Soc 52: 1097–1105, 2015). Let N be a characteristic subgroup of a group …

1. Introduction 1. Introduction Non-Abelian Tensor Absolute Centre Non-Abelian Tensor
Absolute Centre of A Group 1. Introduction Page 1 1. Introduction Let G and H be two groups …

In 1994, Hegarty introduced the notion of $ K (G) $ and $ L (G) $, the autocommutator and
autocentral subgroups of $ G $, respectively. He proved that if ${G}/{L (G)} $ is finite, then so …

The relative Cayley graph of a group G with respect to its proper subgroup H is a graph
whose vertices are elements of G and two vertices h∈ H and g∈ G are adjacent if g= hc for …

Let x be an element of a group G, α∈ Aut (G), n∈ N and A (G)={α∈ Aut (G)| xα (x)= α (x) x,∀
x∈ G}. The autocommutator [x, n α] is defined inductively by [x, α]= x− 1xα= x− 1α (x) and [x …