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NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPS

  • MOGHADDAM, MOHAMMAD REZA R. ;
  • SADEGHIFARD, MOHAMMAD JAVAD
  • Received : 2013.11.20
  • Published : 2015.07.31

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 $2_{\otimes}$-auto Engel groups is introduced and we prove that if G is a $2_{\otimes}$-auto Engel group, then $G{\otimes}$ 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

References

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