Subdirect Product Closed Fitting Classes
In  we pointed out that the class of finite soluble groups whose socle is central is an R 0-closed Fitting class. It follows that if p, q are primes, the class S p S q contains a proper, non-nilpotent, R 0-closed Fitting class. This contrasts with the closure operations S, E ø and, when q|p−1, Q — see  for details and notation. Here we prove
KeywordsNormal Subgroup Finite Group Irreducible Component Nilpotent Group Minimal Normal Subgroup
Unable to display preview. Download preview PDF.
- R.M. Bryant, R.A. Bryce and B. Hartley, “The formation generated by a finite group”, Bull. Austral. Math. Soc. 2 (1970), 347–357, MR43#4901.Google Scholar
- R.A. Bryce and John Cossey, “Metanilpotent Fitting classes”, J. Austral. Math. Soc. (to appear).Google Scholar
- B. Hartley, “On Fischer’s dualization of formation theory”, Proc. London Math. Soc. (3) 19 (1969), 193-207. MR39#5696.Google Scholar