NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPS

Title & Authors
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 $\small{2_{\otimes}}$-auto Engel groups is introduced and we prove that if G is a $\small{2_{\otimes}}$-auto Engel group, then $\small{G{\otimes}}$ 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.
Keywords
non-abelian tensor product;auto-Engel element;autocommutator subgroup;absolute centre;
Language
English
Cited by
References
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