Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D10

Retrieve articles in all journals with MSC: 20D10

Additional Information

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