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Mathematical logic, algebra and number theory
Stone lattices of multiply $\Omega$-canonical Fitting classes
O. V. Kamozina Bryansk state University of engineering and technology, 3, Stanke Dimitrova ave., Bryansk, 241037, Russia
Abstract:
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 $A_i\in\Omega$, $i\in\{ 1,2,\dots,n \}$, $n\in\mathbb N$).
Keywords:
finite group, Fitting class, $\Omega$-canonical Fitting class, lattice of Fitting classes, Stone lattice.
Received December 3, 2018, published September 8, 2020
Citation:
O. V. Kamozina, “Stone lattices of multiply $\Omega$-canonical Fitting classes”, Sib. Èlektron. Mat. Izv., 17 (2020), 1280–1287
Linking options:
https://www.mathnet.ru/eng/semr1288 https://www.mathnet.ru/eng/semr/v17/p1280
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