Let G be a finite soluble group, and let be the Fitting length of G. If φ is a fixed-point-free automorphism of G, that is , we denote by the composition length of . A long-standing conjecture is that , and it is known that this bound is always true if the order of G is coprime to the order of φ. In this paper we find some bounds to in function of without assuming that . In particular we prove the validity of the “universal” bound . This improves the exponential bound known earlier from a special case of a theorem of Dade.
|Data di pubblicazione:||2017|
|Titolo:||The Fitting length of finite soluble groups II: Fixed-point-free automorphisms|
|Rivista:||JOURNAL OF ALGEBRA|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.jalgebra.2017.06.002|
|Appare nelle tipologie:||2.1 Articolo su rivista |