| Yazarlar (4) |
Raimundo Bastos
|
Doç. Dr. Nil MANSUROĞLU
Kırşehir Ahi Evran Üniversitesi, Türkiye |
|
Antonio Tortora
|
|
Maria Tota
|
| Özet |
| Let G be a group, an element g∈ G is called a (left) Engel element if for any x∈ G there exists a positive integer n= n (x, g) such that [x, n_g]= 1, where the commutator [x, n_g] is defined inductively by the rules [x, 1_g]=[x, g] and for n= 2 or n> 2,[x, n_g]=[[x,(n-1) _g], g]. If n can be chosen independently of x, then g is called a (left) n-Engel element or more generally a bounded (left) Engel element. The group G is an Engel group if all its elements are Engel. A subset X of a group is commutator closed if [x, y]∈ X for any x, y∈ X. In this study, we deal with groups generated by commutator closed set of bounded Engel elements. Our main result is to show that a residually finite group which satisfies an identity and is generated by a commutator closed set X of bounded left Engel elements is locally nilpotent. Moreover, we extend such a result to locally graded groups, if X is a normal set. Consequently, we obtain that a locally graded group satisfying an identity, all of whose elements are bounded left Engel, is locally nilpotent. Recall that a group is locally graded if every nontrivial finitely generated subgroup has a proper subgroup of finite index. The class of locally graded groups contains locally groups as well as residually finite groups. |
| Anahtar Kelimeler |
| Bildiri Türü | Tebliğ/Bildiri |
| Bildiri Alt Türü | Özet Metin Olarak Yayınlanan Tebliğ (Uluslararası Kongre/Sempozyum) |
| Bildiri Niteliği | Alanında Hakemli Uluslararası Kongre/Sempozyum |
| Bildiri Dili | İngilizce |
| Kongre Adı | International Conference on Mathematics and Mathematics Education (ICMME-2018) |
| Kongre Tarihi | 27-06-2018 / 29-06-2018 |
| Basıldığı Ülke | |
| Basıldığı Şehir |
