Geodesic
Stone lattices of multiply $\Omega$-canonical Fitting classes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1280-1287.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2020_17_a31,
     author = {O. V. Kamozina},
     title = {Stone lattices of multiply $\Omega$-canonical {Fitting} classes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1280--1287},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a31/}
}
TY  - JOUR
AU  - O. V. Kamozina
TI  - Stone lattices of multiply $\Omega$-canonical Fitting classes
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 1280
EP  - 1287
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a31/
LA  - en
ID  - SEMR_2020_17_a31
ER  - 
%0 Journal Article
%A O. V. Kamozina
%T Stone lattices of multiply $\Omega$-canonical Fitting classes
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 1280-1287
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a31/
%G en
%F SEMR_2020_17_a31
O. V. Kamozina. Stone lattices of multiply $\Omega$-canonical Fitting classes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1280-1287. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a31/

[1] G. Birkhoff, Lattice theory, Nauka, M., 1984 | MR | Zbl

[2] A.N. Skiba, Algebra of formations, Belaruskaya navuka, Minsk, 1997 | MR | Zbl

[3] S. Reifferscheid, On the theory of Fitting classes of finite soluble groups, Dissertation der Mathematischen Fakultat der Eberhard-Karls-Universitat Tubingen zur Erlangung des Grades eines Doktors der Naturwissenschaften, Tubingen, 2001

[4] S. Reifferscheid, “On locally normal Fitting classes of finite soluble groups”, J. Algebra, 261:1 (2003), 186–206 | DOI | MR | Zbl

[5] A.N. Skiba, N.N. Vorob'ev, “On Stone sublattices of the lattice of totally local Fitting classes”, Algebra Discrete Math., 6:4 (2007), 138–146 | MR | Zbl

[6] N.N. Vorob'ev, A.I. Titova, “Stone lattices of multiply $\omega$-local Fitting classes”, Probl. Fiz. Mat. Tekh., 2017:4(33) (2017), 48–52 | MR | Zbl

[7] N.N. Vorob'ev, A.P. Mekhovich, “On Stone lattices of multiply saturated formations”, Vestnik VDU, 4(70) (2012), 20–23

[8] V.A. Vedernikov, “Maximal satellites of $\Omega$-foliated formations and Fitting classes”, Proceedings of the Steklov Institute of Mathematics, 2, Supplementary issues (2001), S217–S233 | MR | Zbl

[9] V.A. Vedernikov, M.M. Sorokina, “$\Omega$-foliated formations and Fitting classes of finite groups”, Discrete Math. Appl., 11:5 (2001), 507–527 | DOI | MR | Zbl

[10] M.M. Sorokina, “On minimal satellites of $\Omega$-foliated Fitting classes and formations of finite groups”, Collection of scientific papers BGPU – 70 years, 2000, 199–203

[11] K. Doerk, T. Nawkes, Finite soluble groups, Walter de Gruyter, Berlin etc, 1992 | MR | Zbl

[12] N.N. Vorob'ev, A.N. Skiba, “On Boolean lattices of $n$-multiply local Fitting classes”, Siberian Math. J., 40:3 (1999), 446–452 | DOI | MR

[13] O.V. Kamozina, “Boolean lattices of $n$-multiply $\Omega$-bicanonical Fitting classes”, Discrete Math. Appl., 12:5 (2002), 483–489 | DOI | MR | Zbl

[14] O.V. Kamozina, “On Boolean lattices of multiply $\Omega$-foliated Fitting classes”, Questions of algebra, 18 (2002), 134–137 | MR | Zbl

[15] V.E. Egorova, “Critical non-singly-generated totally canonical Fitting classes of finite groups”, Math. Notes, 83:4 (2008), 478–484 | DOI | MR | Zbl