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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a sublattice of the lattice of normal Fitting classes
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by A. R. Makan PDF
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.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 46 (1974), 199-204
  • MSC: Primary 20D10
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0352251-7
  • MathSciNet review: 0352251