scholarly journals A Class of infinite soluble groups with an A-group condition

1980 ◽  
Vol 21 (1) ◽  
pp. 81-84
Author(s):  
M. J. Tomkinson
Keyword(s):  
Homomorphic Image ◽  
Finite Groups ◽  
Locally Finite ◽  
Soluble Groups ◽  
Sylow Subgroups ◽  
Locally Finite Groups ◽  
Group Condition

Finite soluble groups in which all the Sylow subgroups are abelian were first investigated by Taunt [8] who referred to them as A-groups. Locally finite groups with the same property have been considered by Graddon [2]. By the use of Sylow theorems it is clear that every section (homomorphic image of a subgroup) of an A-group is also an A-group and hence every nilpotent section of an A-group is abelian. This is the characterization that we use here in considering groups which are not, in general, periodic.

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.

Local systems and Sylow subgroups in locally finite groups. II

1974 ◽  
Vol 75 (1) ◽  
pp. 1-22 ◽  
Author(s):  
A. Rae
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Local System ◽  
The Other ◽  
Locally Finite Group ◽  
Local Systems ◽  
Locally Finite ◽  
Sylow Subgroups ◽  
Locally Finite Groups ◽  
Other Hand

1.1. Introduction. In this paper, we continue with the theme of (1): the relationships holding between the Sπ (i.e. maximal π) subgroups of a locally finite group and the various local systems of that group. In (1), we were mainly concerned with ‘good’ Sπ subgroups – those which reduce into some local system (and are said to be good with respect to that system). Here, on the other hand, we are concerned with a very much more special sort of Sπ subgroup.

Formation theory and groups of automorphisms of -groups

1977 ◽  
Vol 76 (4) ◽  
pp. 255-265 ◽  
Author(s):  
M. J. Tomkinson
Keyword(s):  
Finite Groups ◽  
Composition Series ◽  
Formation Theory ◽  
Locally Finite ◽  
Soluble Groups ◽  
Locally Finite Groups ◽  
Group Of Automorphisms ◽  
Infinite Case ◽  
Groups Of Automorphisms ◽  
Automorphisms Of Groups

SynopsisFurther results from the theory of finite soluble groups are extended to the class of locally finite groups with a satisfactory Sylow structure. Let be a saturated U-formation and A a -group of automorphisms of the -group G. A is said to act -centrally on G if G has an A-composition series (Λσ/Vσ; σ ∈ ∑) such that A induces an f(p)-group of automorphisms in each p-factor Λσ/Vσ. We show that in this situation A is an -group, thus generalising the result of Schmid [8]. Associated results of Schmid and of Baer are also extended to the infinite case.

Local systems and Sylow subgroups in locally finite groups. I

1972 ◽  
Vol 72 (2) ◽  
pp. 141-160 ◽  
Author(s):  
A. Rae
Keyword(s):  
Finite Groups ◽  
Finite Subset ◽  
Local System ◽  
Local Systems ◽  
Locally Finite ◽  
Sylow Subgroups ◽  
Locally Finite Groups

1. Introduction. By a local system for a group G we shall mean a collection Σ of subgroups of G such that for every finite subset of G there is a member of Σ containing it. If is a class of groups G is locally if G has a local system of subgroups.

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