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