NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPS

作者：Moghaddam Mohammad Reza R^*; Sadeghifard Mohammad Javad

来源：Bulletin of the Korean Mathematical Society, 2015, 52(4): 1097-1105.

DOI：10.4134/BKMS.2015.52.4.1097

• non-abelian tensor product
• auto-Engel element
• autocommutator subgroup
• absolute centre

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 2(circle times)-auto Engel groups is introduced and we prove that if G is a 2(circle times)-auto Engel group, then G 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.

• 出版日期2015-7