Sugli automorfismi uniformi e privi di coincidenze dei gruppi infiniti

Jabara, Enrico

Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 2, pp. 501-510

Résumé

Let $\Phi$ be a group of automorphisms of the group $(N, +)$ such that for every $\phi \in \Phi \setminus \{1\}$ the map $T_{\phi} \colon N \to N$$x \mapsto -x + \phi(x)$ is bijective. In this paper we prove that if $N$ is infinite and it is union of a finite number of $\Phi$-orbits, then $N$ is abelian.