On the Boolean lattices ofn times local fitting classes

1999 ◽  
Vol 40 (3) ◽  
pp. 446-452
Author(s):  
N. N. Vorob′ëv ◽  
A. N. Skiba
Keyword(s):  
Boolean Lattices ◽  
Fitting Classes ◽  
Local Fitting

scholarly journals Quasinormal Fitting classes of finite groups

2019 ◽  
pp. 18-26
Author(s):  
Martsinkevich Anna V.
Keyword(s):  
Natural Number ◽  
Wreath Product ◽  
Cyclic Group ◽  
Finite Groups ◽  
Fitting Class ◽  
Soluble Groups ◽  
Normal Fitting Class ◽  
Fitting Classes ◽  
Local Fitting ◽  
Class F

Let P be the set of all primes, Zn a cyclic group of order n and X wr Zn the regular wreath product of the group X with Zn. A Fitting class F is said to be X-quasinormal (or quasinormal in a class of groups X ) if F ⊆ X, p is a prime, groups G ∈ F and G wr Zp ∈ X, then there exists a natural number m such that G m wr Zp ∈ F. If  X is the class of all soluble groups, then F is normal Fitting class. In this paper we generalize the well-known theorem of Blessenohl and Gaschütz in the theory of normal Fitting classes. It is proved, that the intersection of any set of nontrivial X-quasinormal Fitting classes is a nontrivial X-quasinormal Fitting class. In particular, there exists the smallest nontrivial X-quasinormal Fitting class. We confirm a generalized version of the Lockett conjecture (in particular, the Lockett conjecture) about the structure of a Fitting class for the case of X-quasinormal classes, where X is a local Fitting class of partially soluble groups.

On σ-local Fitting classes

2020 ◽  
Vol 542 ◽  
pp. 116-129 ◽  
Author(s):  
Wenbin Guo ◽  
Li Zhang ◽  
N.T. Vorob'ev
Keyword(s):  
Fitting Classes ◽  
Local Fitting

scholarly journals A characterization of dominant local Fitting classes

2012 ◽  
Vol 358 ◽  
pp. 27-32 ◽  
Author(s):  
P. Hauck ◽  
V.N. Zahursky
Keyword(s):  
Fitting Classes ◽  
Local Fitting

On the distributivity of the lattice of solvable totally local fitting classes

2000 ◽  
Vol 67 (5) ◽  
pp. 563-571 ◽  
Author(s):  
N. N. Vorob’ev ◽  
A. N. Skiba
Keyword(s):  
Fitting Classes ◽  
Local Fitting

Maximal subclasses of local fitting classes

2008 ◽  
Vol 49 (6) ◽  
pp. 1124-1130 ◽  
Author(s):  
N. V. Savelyeva ◽  
N. T. Vorob’ev
Keyword(s):  
Fitting Classes ◽  
Local Fitting

Boolean lattices of n-multiply Ω-bicanonical Fitting classes

2002 ◽  
Vol 12 (5) ◽  
Author(s):  
O.V. Kamozina
Keyword(s):  
Boolean Lattice ◽  
Direct Decomposition ◽  
Fitting Class ◽  
Boolean Lattices ◽  
Fitting Classes ◽  
Direct Decompositions

AbstractWe describe the n-multiply Ω-bicanonical Fitting classes with Boolean lattice of Fitting subclasses. In particular, it is shown that in this case a Fitting class is directly decomposable with the use of the set of all atoms of its lattice. Here the notion of a direct decomposition plays the key role. Therefore we study direct decompositions separately and consider Ω-foliated Fitting classes with more general directions.

Lattices of partially local fitting classes

2009 ◽  
Vol 50 (6) ◽  
pp. 1038-1044 ◽  
Author(s):  
E. N. Zalesskaya ◽  
N. N. Vorob’ëv
Keyword(s):  
Fitting Classes ◽  
Local Fitting

Active contour segmentation model of combining global and dual-core local fitting energy

2013 ◽  
Vol 33 (4) ◽  
pp. 1092-1095 ◽  
Author(s):  
Jie ZHAO ◽  
Yongmei QI ◽  
Zhengyong PAN
Keyword(s):  
Active Contour ◽  
Contour Segmentation ◽  
Dual Core ◽  
Local Fitting

On Boolean Lattices of Module Classes

2018 ◽  
Vol 25 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Alejandro Alvarado-García ◽  
César Cejudo-Castilla ◽  
Hugo Alberto Rincón-Mejía ◽  
Ivan Fernando Vilchis-Montalvo ◽  
Manuel Gerardo Zorrilla-Noriega
Keyword(s):  
Torsion Theory ◽  
Boolean Lattices

Some properties of and relations between several (big) lattices of module classes are used in this paper to obtain information about the ring over which modules are taken. The authors reach characterizations of trivial rings, semisimple rings and certain rings over which every torsion theory is hereditary.

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