On a sublattice of the lattice of normal Fitting classes

Makan, A. R.

doi:10.1090/S0002-9939-1974-0352251-7

On a sublattice of the lattice of normal Fitting classes
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Proc. Amer. Math. Soc. 46 (1974), 199-204 Request permission

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.

References

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Fitting classes with the wreath product property are normal

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