Approximability of finite rank soluble groups by certain classes of finite groups

2014 ◽  
Vol 58 (8) ◽  
pp. 15-23 ◽  
Author(s):  
D. N. Azarov
Keyword(s):  
Finite Groups ◽  
Finite Rank ◽  
Soluble Groups

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.

SOLUBLE GROUPS OF FINITE RANK

2004 ◽  
pp. 83-104
Author(s):  
John C. Lennox ◽  
Derek J. S. Robinson
Keyword(s):  
Finite Rank ◽  
Soluble Groups

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.

scholarly journals On soluble groups of module automorphisms of finite rank

2017 ◽  
Vol 67 (3) ◽  
pp. 809-818 ◽  
Author(s):  
Bertram A. F. Wehrfritz
Keyword(s):  
Finite Rank ◽  
Soluble Groups

Locally Finite Groups with Centralizers of Finite Rank

2016 ◽  
Vol 44 (12) ◽  
pp. 5074-5087 ◽  
Author(s):  
Kıvanc̣ Ersoy ◽  
Chander Kanta Gupta
Keyword(s):  
Finite Groups ◽  
Finite Rank ◽  
Locally Finite ◽  
Locally Finite Groups

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.

scholarly journals Groups which satisfy a weak form of Poincaré duality

1991 ◽  
Vol 34 (3) ◽  
pp. 463-486
Author(s):  
J. E. Roberts
Keyword(s):  
Finite Rank ◽  
Weak Form ◽  
Homological Dimension ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Soluble Groups ◽  
Finite Dimensional ◽  
Duality Property ◽  
The Given ◽  
Torsion Free

Our main result is that a “restricted Poincaré duality” property with respect to finite dimensional coefficient modules over a field holds for a certain class of groups which includes all soluble groups of finite Hirsch length. This relies on a generalisation to the given class of a module construction by Stammbach; an extension of his result on homological dimension to these groups is given. We also generalise the well-known result that torsion-free soluble groups of finite rank are countable.

Locally (soluble-by-finite) groups with all proper insoluble subgroups of finite rank

1997 ◽  
Vol 68 (2) ◽  
pp. 100-109 ◽  
Author(s):  
Martyn R. Dixon ◽  
Martin J. Evans ◽  
Howard Smith
Keyword(s):  
Finite Groups ◽  
Finite Rank
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