Computing Projectors, Injectors, Residuals and Radicals of Finite Soluble Groups

✍ Scribed by Burkhard Höfling

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 348 KB
• Volume: 32
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.2001.0477

✦ Synopsis

Let G be a finite soluble group, given by a polycyclic generating system, and X a class of groups, represented by an algorithm that decides whether a given finite group belongs to X or not. This paper contains practical algorithms for the computation of X-projectors and X-injectors of G, where X is an arbitrary Schunck class or Fitting class, respectively. It also describes algorithms for computing X-radicals for Fitting classes X and X-residuals for formations X. Variants of the latter algorithms can be used to compute all normal (X-)subgroups and the socle of G.