On saturated formations, theta-pairs and completions in finite groups

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.

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Schunck classes and projectors in a class of locally finite groups

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500019301 ◽

1995 ◽

Vol 38 (3) ◽

pp. 511-522 ◽

Cited By ~ 6

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.

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ON SYLOW NORMALIZERS OF FINITE GROUPS

Journal of Algebra and Its Applications ◽

10.1142/s0219498813501168 ◽

2013 ◽

Vol 13 (03) ◽

pp. 1350116 ◽

Cited By ~ 1

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.

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On Lattices of Formations of Finite Groups

Algebra Colloquium ◽

10.1142/s1005386710000532 ◽

2010 ◽

Vol 17 (04) ◽

pp. 557-564 ◽

Cited By ~ 7

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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