Algebraic lattices of partially saturated formations of finite groups

2019 ◽  
Vol 31 (3-4) ◽  
pp. 701-707 ◽  
Author(s):  
Aleksandr Tsarev
Keyword(s):  
Finite Groups ◽  
Partially Saturated ◽  
Algebraic Lattices ◽  
Saturated Formations

On partially saturated formations of finite groups

2007 ◽  
Vol 198 (6) ◽  
pp. 757-775 ◽  
Author(s):  
Adolfo Ballester-Bolinches ◽  
Clara Calvo ◽  
L A Shemetkov
Keyword(s):  
Finite Groups ◽  
Partially Saturated ◽  
Saturated Formations

ON LAWS OF LATTICES OF PARTIALLY SATURATED FORMATIONS

2009 ◽  
Vol 02 (01) ◽  
pp. 155-169 ◽  
Author(s):  
Leonid A. Shemetkov ◽  
Alexander N. Skiba ◽  
Nikolay N. Vorob'ev
Keyword(s):  
Natural Number ◽  
Finite Groups ◽  
Partially Saturated ◽  
Subgroup Functor ◽  
Saturated Formations

It is proved that every law of the lattice of all τ-closed formations of finite groups is fulfilled in the lattice of all τ-closed n-multiply ω-saturated formations of finite groups, for every subgroup functor τ and every natural number n.

scholarly journals Frattini classes of saturated formations of finite groups

1990 ◽  
Vol 42 (2) ◽  
pp. 267-286 ◽  
Author(s):  
Peter Förster
Keyword(s):  
Finite Groups ◽  
Local Formation ◽  
Formation Of Finite Groups ◽  
Saturated Formations ◽  
Definition Of

We study the following question: given any local formation of finite groups, do there exist maximal local subformations? An answer is given by providing a local definition of the intersection of all maximal local subformations.

scholarly journals Schunck classes and projectors in a class of locally finite groups

1995 ◽  
Vol 38 (3) ◽  
pp. 511-522 ◽  
Author(s):  
M. J. Tomkinson
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Locally Finite ◽  
Soluble Groups ◽  
Locally Finite Groups ◽  
Finite Case ◽  
Saturated Formations ◽  
Definition Of ◽  
Schunck Class

We introduce a definition of a Schunck class of periodic abelian-by-finite soluble groups using major subgroups in place of the maximal subgroups used in Finite groups. This allows us to develop the theory as in the finite case proving the existence and conjugacy of projectors. Saturated formations are examples of Schunck classes and we are also able to obtain an infinite version of Gaschütz Ω-subgroups.

ON SYLOW NORMALIZERS OF FINITE GROUPS

2013 ◽  
Vol 13 (03) ◽  
pp. 1350116 ◽  
Author(s):  
L. S. KAZARIN ◽  
A. MARTÍNEZ-PASTOR ◽  
M. D. PÉREZ-RAMOS
Keyword(s):  
Finite Groups ◽  
Property A ◽  
Soluble Groups ◽  
Sylow Subgroups ◽  
Hall Subgroups ◽  
Saturated Formations ◽  
The Universe ◽  
Do So

The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent Hall subgroups for given sets of primes are exactly the subgroup-closed saturated formations satisfying the following property: a group belongs to the class if and only if its Sylow normalizers do so. The paper analyzes the extension of this research to the universe of all finite groups.

On Lattices of Formations of Finite Groups

2010 ◽  
Vol 17 (04) ◽  
pp. 557-564 ◽  
Author(s):  
L. A. Shemetkov ◽  
A. N. Skiba ◽  
N. N. Vorob'ev
Keyword(s):  
Finite Groups ◽  
Saturated Formations

Let ω be a set of primes with |ω| > 1, and m > n ≥ 0 be integers. It is proved that the lattice of all τ-closed m-multiply ω-saturated formations is not a sublattice of the lattice of all τ-closed n-multiply ω-saturated formations.

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