Formations of finite monoids and their applications: formations of languages and $$\tau $$-closed saturated formations of finite groups

2019 ◽  
Vol 65 (2) ◽  
pp. 369-374 ◽  
Author(s):  
Aleksandr Tsarev
Keyword(s):  
Finite Groups ◽  
Finite Monoids ◽  
Saturated Formations

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.

PARABOLIC SUBGROUPS AND CUSPIDAL REPRESENTATIONS OF FINITE MONOIDS

1991 ◽  
Vol 01 (01) ◽  
pp. 33-47 ◽  
Author(s):  
JAN OKNIŃSKI ◽  
MOHAN S. PUTCHA
Keyword(s):  
Inverse Semigroup ◽  
Finite Groups ◽  
Special Class ◽  
Semigroup Algebra ◽  
Parabolic Subgroups ◽  
Finite Monoids ◽  
Representations Of Finite Groups ◽  
Symmetric Inverse Semigroup ◽  
Complex Semigroup ◽  
Cuspidal Representations

This paper is mostly concerned with arbitrary finite monoids M with the complex semigroup algebra [Formula: see text] semisimple. Using the 1942 work of Clifford, we develop for these monoids a theory of cuspidal representations. Harish-Chandra's philosophy of cuspidal representations of finite groups can then be derived with an appropriate specialization. For [Formula: see text], we use Solomon's Hecke algebra to obtain a correspondence between the 'simple' representations of [Formula: see text] and the representations of the symmetric inverse semigroup. We also prove a semisimplicity theorem for a special class of finite monoids of the type which was earlier used by the authors to prove the semisimplicity of [Formula: see text].

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.

OnG-Covering Subgroup Systems for Some Saturated Formations of Finite Groups

2013 ◽  
Vol 41 (8) ◽  
pp. 2948-2956 ◽  
Author(s):  
Wenbin Guo ◽  
Jianhong Huang ◽  
Alexander N. Skiba
Keyword(s):  
Finite Groups ◽  
Saturated Formations

On semidirectly closed non-aperiodic pseudovarieties of finite monoids

2020 ◽  
Vol 63 (4) ◽  
pp. 913-928
Author(s):  
Jiří Kaďourek
Keyword(s):  
Prime Number ◽  
Finite Groups ◽  
Complete Lattice ◽  
Solvable Groups ◽  
Finite Monoids ◽  
The Continuum

AbstractIt is shown that, for every prime number p, the complete lattice of all semidirectly closed pseudovarieties of finite monoids whose intersection with the pseudovariety G of all finite groups is equal to the pseudovariety Gp of all finite p-groups has the cardinality of the continuum. Furthermore, it is shown, in addition, that the complete lattice of all semidirectly closed pseudovarieties of finite monoids whose intersection with the pseudovariety G of all finite groups is equal to the pseudovariety Gsol of all finite solvable groups has also the cardinality of the continuum.

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