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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⊗-auto Engel groups is introduced and we prove that if G is a 2⊗-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.
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참고문헌 (12)
참고문헌 신청
D. P. Biddle / 2003 / On subgroups related to the tensor center / Glasg. Math. J 45 (2) : 323 ~ 332
M. M. Nasrabadi / 2012 / On non abelian tensor analogues of 3-Engel groups / Indag. Math 23 (3) : 337 ~ 340
M. M. Nasrabadi / 2013 / On some subgroups associated with the tensor square of a group / Int. J. Group Theory 2 (2) : 25 ~ 33
M. Naghshineh / 2009 / Third term of the lower auto-central series of abelian groups / J. Math. Ext 4 (1) : 1 ~ 6
M. R. R. Moghaddam / / Some Properties of 2-auto Engel groups, to appear in Quaestiones Mathematicae
M. M. Nasrabadi / 2012 / On non abelian tensor analogues of 3-Engel groups / Indag. Math 23 (3) : 337 ~ 340
M. M. Nasrabadi / 2013 / On some subgroups associated with the tensor square of a group / Int. J. Group Theory 2 (2) : 25 ~ 33
M. Naghshineh / 2009 / Third term of the lower auto-central series of abelian groups / J. Math. Ext 4 (1) : 1 ~ 6
M. R. R. Moghaddam / / Some Properties of 2-auto Engel groups, to appear in Quaestiones Mathematicae
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