Groupes $n$-abéliens généralisés
Abdollahi, A. ; Daoud, B. ; Endimioni, G.
Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, p. 287-294 / Harvested from Project Euclid
Let $n$ be an integer $\geqslant 2$. A group $G$ is called generalized $n$-abelian if it admits a {\em positive polynomial} endomorphism of degree $n$, that is if there exist $n$ elements $a_1, a_2, \dots, a_n$ of $G$ such that the function $\varphi: x\mapsto x^{a_1}x^{a_2}\cdots x^{a_n}$ is an endomorphism of $G$. In this paper we give some sufficient conditions for a generalized $n$-abelian group to be abelian. In particular, we show that every group admitting a positive polynomial monomorphism of degree 3 is abelian.
Publié le : 2006-06-14
Classification:  Polynomial automorphisms,  $n$-abelian groups,  20D45,  20D15
@article{1148059463,
     author = {Abdollahi, A. and Daoud, B. and Endimioni, G.},
     title = {Groupes $n$-ab\'eliens g\'en\'eralis\'es},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {12},
     number = {5},
     year = {2006},
     pages = { 287-294},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/1148059463}
}
Abdollahi, A.; Daoud, B.; Endimioni, G. Groupes $n$-abéliens généralisés. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp.  287-294. http://gdmltest.u-ga.fr/item/1148059463/