NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPS

Abstract

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 G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of <TEX>$2_{\otimes}$</TEX>-auto Engel groups is introduced and we prove that if G is a <TEX>$2_{\otimes}$</TEX>-auto Engel group, then <TEX>$G{\otimes}$</TEX> Aut(G) is abelian. Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.