On Non-Abelian Tensor Analogues of 3-Engel and 4-Engel Groups
| Autor: | Azam Hokmabadi, Hanieh Golmakani, Elaheh Mohammadzadeh, Fahimeh Mohammadzadeh |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 43:4415-4421 |
| ISSN: | 1532-4125 0092-7872 |
| Popis: | A group G is said to be an n ⊗-Engel, if [y, n−1 x] ⊗ x = 1 for all x, y ∈ G, and we say a group G is tensor nilpotent of class at most n, if . In this article, we show that if G is a 3⊗-Engel group, then ⟨ x, x y ⟩ is tensor nilpotent of class at most 2, for all x, y ∈ G. We also prove that if G is a 4⊗-Engel group and G ⊗ G is torsion-free, then ⟨ x, x y ⟩ is tensor nilpotent of class at most 4, for all x, y ∈ G. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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