Some Notes on Relative Commutators
| Autor: | Ahmad Erfanian, Masoumeh Ganjali |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | InPrime: Indonesian Journal of Pure and Applied Mathematics. 2:65-70 |
| ISSN: | 2716-2478 2686-5335 |
| DOI: | 10.15408/inprime.v2i2.14482 |
| Popis: | Let G be a group and α ϵ Aut ( G ). An α -commutator of elements x , y ϵ G is defined as [x, y] α = x -1 y -1 xy α . In 2015, Barzegar et al. introduced an α -commutator of elements of G and defined a new generalization of nilpotent groups by using the definition of α -commutators which is called an α -nilpotent group. They also introduced an α -commutator subgroup of G , denoted by D α ( G ) which is a subgroup generated by all α -commutators. In 2016, an α -perfect group, a group that is equal to its α -commutator subgroup, was introduced by authors of this paper and the properties of such group was investigated. They proved some results on α -perfect abelian groups and showed that a cyclic group G of even order is not α -perfect for any α ϵ Aut ( G ). In this paper, we may continue our investigation on α -perfect groups and in addition to studying the relative perfectness of some classes of finite p -groups, we provide an example of a non-abelian α -perfect 2-group. |
| Databáze: | OpenAIRE |
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