SPLITTING OVER THE LOCALLY NILPOTENT RESIDUAL FOR A CLASS OF LOCALLY FINITE GROUPS

1976 ◽  
Vol 27 (4) ◽  
pp. 395-400 ◽  
Author(s):  
B. HARTLEY
Keyword(s):  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Locally Nilpotent ◽  
Nilpotent Residual

scholarly journals On locally finite groups factorized by locally nilpotent subgroups

1996 ◽  
Vol 106 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Silvana Franciosi ◽  
Francesco de Giovanni ◽  
Yaroslav P. Sysak
Keyword(s):  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Locally Nilpotent

Splitting over nilpotent and hypercentral residuals

1975 ◽  
Vol 78 (2) ◽  
pp. 215-226 ◽  
Author(s):  
B. Hartley ◽  
M. J. Tomkinson
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Formation Theory ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Nilpotent Residual ◽  
A Finite Group

It is a well known theorem of Gaschütz (4) and Schenkman (12) that if G is a finite group whose nilpotent residual A is Abelian, then G splits over A and the complements to A in G are conjugate. Following Robinson (10) we describe this situation by saying that G splits conjugately over A. A number of generalizations of this result have since been obtained, some of them being in the context of the formation theory of finite or locally finite groups (see, for example, (1), (3)) and others, for example, the recent and far-reaching results of Robinson (10, 11) being concerned with groups which are not necessarily periodic. Our results here are of the latter type.

On Groups Saturated with Abelian Subgroups

1998 ◽  
Vol 08 (04) ◽  
pp. 443-466 ◽  
Author(s):  
Lev S. Kazarin ◽  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Finite Groups ◽  
Abelian Groups ◽  
Normal Subgroups ◽  
Main Subject ◽  
Maximal Condition ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Locally Nilpotent ◽  
Abelian Subgroups ◽  
Weak Maximal Condition

Groups with the weak maximal condition on non-abelian subgroups are the main subject of this research. Locally finite groups with this property are abelian or Chemikov. Non-abelian groups with the weak maximal condition on non-abelian subgroups, which have an ascending series of normal subgroups with locally nilpotent or locally finite factors, are described in this article.

Basis normalizers and Carter subgroups in a class of locally finite groups

1972 ◽  
Vol 71 (2) ◽  
pp. 189-198 ◽  
Author(s):  
C. J. Graddon ◽  
B. Hartley
Keyword(s):  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Finite Series ◽  
Locally Nilpotent ◽  
Image Position

We shall be working throughout this paper in the class of locally finite groups introduced in (3) and further discussed in (5) and (6), and all groups appearing will be assumed to belong to this class. By definition, is the largest subgroupclosed class of locally finite groups satisfying the conditions:U1. If G ε then G has a finite serieswith locally nilpotent factors.

scholarly journals Uncountable existentially closed groups in locally finite group classes

1990 ◽  
Vol 32 (2) ◽  
pp. 153-163 ◽  
Author(s):  
Felix Leinen
Keyword(s):  
Finite Group ◽  
Wreath Product ◽  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Existentially Closed ◽  
Fixed Set ◽  
Locally Nilpotent ◽  
Closed Groups ◽  
Restrictive Type

In this paper, will always denote a local class of locally finite groups, which is closed with respect to subgroups, homomorphic images, extensions, and with respect to cartesian powers of finite -groups. Examples for x are the classes L ℐπ of all locally finite π-groups and L(ℐπ ∩ ) of all locally soluble π-groups (where π is a fixed set of primes). In [4], a wreath product construction was used in the study of existentially closed -groups (=e.c. -groups); the restrictive type of construction available in [4] permitted results for only countable groups. This drawback was then removed partially in [5] with the help of permutational products. Nevertheless, the techniques essentially only permitted amalgamation of -groups with locally nilpotent π-groups. Thus, satisfactory results could be obtained for Lp-groups (resp. locally nilpotent π-groups) [6], while the theory remained incomplete in all other cases.

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

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