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Normal Fitting classes and Hall subgroups [PDF]

Bulletin of the Australian Mathematical Society, 1980
It was shown by Bryce and Cossey that each Hall π-subgroup of a group in the smallest normal Fitting class S* necessarily lies in S*, for each set of primes π. We prove here that for each set of primes π such that |π| ≥ 2 and π′ is not empty, there exists a normal Fitting class without this closure property. A characterisation is obtained of all normal
E. Cusack
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On a Sublattice of the Lattice of Normal Fitting Classes [PDF]

Proceedings of the American Mathematical Society, 1974
Let L {\mathbf {L}} be the set of all Fitting classes F \mathfrak {F} with the following two properties: (i) F ⊇ N \mathfrak {F} \supseteq \mathfrak {N} , the class of all finite nilpotent groups, and (ii)
A. Makan
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Fitting classes based on groups of nilpotent length three with operator-isomorphic minimal normal subgroups [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1991
AbstractIn this paper a technique for constructing Fitting Classes is applied to certain groups of nilpotent length three which have non-unique minimal normal subgroups. A characterisation of the minimal Fitting Class of some of these groups is also given.
B. McCann
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On locally normal Fitting classes of finite soluble groups

Journal of Algebra, 2003
A generalization of the concept of normal Fitting classes introduced by Blessenohl and Gaschütz arises in the following way: Let \(\mathcal X\) and \(\mathcal F\) be non-trivial Fitting classes of finite soluble groups such that \({\mathcal X}\subseteq{\mathcal F}\).
S. Reifferscheid
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Normal Fitting classes of finite groups [PDF]