Gruppi Policiclici Dotati di un Automorfismo Uniforme di Ordinepq |
| |
Authors: | Enrico Jabara |
| |
Affiliation: | (1) Dipartimento di Matematica Applicata, Università CA’ Foscari di Venezia, Cà Dolfin Dorsoduro 3825/E, 30123, Venezia |
| |
Abstract: | An automorphismϕ of a groupG is said to be uniform il for everyg ∈G there exists anh ∈G such thatG=h −1 h ρ . It is a well-known fact that ifG is finite, an automorphism ofG is uniform if and only if it is fixed-point-free. In [7] Zappa proved that if a polycyclic groupG admits an uniform automorphism of prime orderp thenG is a finite (nilpotent)p′-group. In this paper we continue Zappa’s work considering uniform automorphism of orderpg (p andq distinct prime numbers). In particular we prove that there exists a constantμ (depending only onp andq) such that every torsion-free polycyclic groupG admitting an uniform automorphism of orderpq is nilpotent of class at mostμ. As a consequence we prove that if a polycyclic groupG admits an uniform automorphism of orderpq thenZ μ (G) has finite index inG. Al professore Guido Zappa per il suo 900 compleanno |
| |
Keywords: | Uniform automorphisms polycyclic groups |
本文献已被 SpringerLink 等数据库收录! |