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Subdirect Product Closed Fitting Classes

  • R. A. Bryce
  • John Cossey
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 372)

Abstract

In [2] 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 [2] for details and notation. Here we prove

Keywords

Normal Subgroup Finite Group Irreducible Component Nilpotent Group Minimal Normal Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    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
  2. [2]
    R.A. Bryce and John Cossey, “Metanilpotent Fitting classes”, J. Austral. Math. Soc. (to appear).Google Scholar
  3. [3]
    B. Hartley, “On Fischer’s dualization of formation theory”, Proc. London Math. Soc. (3) 19 (1969), 193-207. MR39#5696.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • R. A. Bryce
    • 1
  • John Cossey
    • 1
  1. 1.Australian National UniversityCanberraAustralia

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