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Subdirect Product Closed Fitting Classes

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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. 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.

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  2. R.A. Bryce and John Cossey, “Metanilpotent Fitting classes”, J. Austral. Math. Soc. (to appear).

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  3. B. Hartley, “On Fischer’s dualization of formation theory”, Proc. London Math. Soc. (3) 19 (1969), 193-207. MR39#5696.

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© 1974 Springer-Verlag Berlin Heidelberg

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Bryce, R.A., Cossey, J. (1974). Subdirect Product Closed Fitting Classes. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_13

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  • DOI: https://doi.org/10.1007/978-3-662-21571-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06845-7

  • Online ISBN: 978-3-662-21571-5

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