Stone lattices of multiply $\Omega$-canonical Fitting classes

O. V. Kamozina

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1280-1287

Résumé

Let $L$ be a lattice with $0$ and $1$. A distributive lattice $L$ with pseudocomplements, each element of which satisfies an identity $a^{\circ}\vee (a^{\circ} )^{\circ} =1$, where $a^{\circ}$ is a pseudocomplement of an element $a$, is called a Stone lattice. The article describes multiply $\Omega$-canonical Fitting classes with a Stone lattice of multiply $\Omega$-canonical Fitting subclasses. It is shown that such Fitting classes are subclasses of the class $\mathfrak{D}_\Omega =\times_{A \in \Omega} \mathfrak{G}_A=(B_1 \times B_2 \times \dots \times B_n$ : $ B_i \in \mathfrak{G}_{A_i}$ for some $A_i\in\Omega$, $i\in\{ 1,2,\dots,n \}$, $n\in\mathbb N$).

Détail

Keywords: finite group, Fitting class, $\Omega$-canonical Fitting class, lattice of Fitting classes, Stone lattice.