Existentially closed locally finite central extensions; Multipliers and local systems

1984 ◽  
Vol 187 (3) ◽  
pp. 383-392 ◽  
Author(s):  
Richard E. Phillips
Keyword(s):  
Central Extensions ◽  
Local Systems ◽  
Locally Finite ◽  
Existentially Closed

Existentially closed central extensions of locally finite p-groups

1986 ◽  
Vol 100 (2) ◽  
pp. 281-301 ◽  
Author(s):  
Felix Leinen ◽  
Richard E. Phillips
Keyword(s):  
Central Extensions ◽  
Locally Finite ◽  
Existentially Closed ◽  
Image Position

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

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.

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.

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.

scholarly journals EXISTENTIALLY CLOSED BROUWERIAN SEMILATTICES

2019 ◽  
Vol 84 (4) ◽  
pp. 1544-1575
Author(s):  
LUCA CARAI ◽  
SILVIO GHILARDI
Keyword(s):  
Locally Finite ◽  
Existentially Closed ◽  
Model Completion

AbstractThe variety of Brouwerian semilattices is amalgamable and locally finite; hence, by well-known results [19], it has a model completion (whose models are the existentially closed structures). In this article, we supply a finite and rather simple axiomatization of the model completion.

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