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Groupes $n$-abéliens généralisés
- Source :
- Bull. Belg. Math. Soc. Simon Stevin 13, no. 2 (2006), 287-294, Scopus-Elsevier
- Publication Year :
- 2006
- Publisher :
- The Belgian Mathematical Society, 2006.
-
Abstract
- 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.
Details
- Language :
- French
- Database :
- OpenAIRE
- Journal :
- Bull. Belg. Math. Soc. Simon Stevin 13, no. 2 (2006), 287-294, Scopus-Elsevier
- Accession number :
- edsair.doi.dedup.....8de3bebf70205c7c3e809c51a338e9e6