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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On a sublattice of the lattice of normal Fitting classes

Author: A. R. Makan
Journal: Proc. Amer. Math. Soc. 46 (1974), 199-204
MSC: Primary 20D10
MathSciNet review: 0352251
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Abstract: Let $ {\mathbf{L}}$ be the set of all Fitting classes $ \mathfrak{F}$ with the following two properties: (i) $ \mathfrak{F} \supseteq \mathfrak{N}$, the class of all finite nilpotent groups, and (ii) every $ \mathfrak{F}$-avoided, complemented chief factor of any finite soluble group $ G$ is partially $ \mathfrak{F}$-complemented in $ G$. It is shown that $ {\mathbf{L}}$ is a complete sublattice of the complete lattice $ {\mathbf{N}}$ of all nontrivial normal Fitting classes, and, moreover, it is lattice isomorphic to the subgroup lattice of the Frattini factor group of a certain abelian torsion group due to H. Lausch.

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Keywords: Normal Fitting class, injector, normal Fitting pair, complete lattice, standard and twisted wreath products
Article copyright: © Copyright 1974 American Mathematical Society