scholarly journals ON THE STRUCTURE OF GROUPS ENDOWED WITH A COMPATIBLE C-RELATION

2018 ◽  
Vol 83 (3) ◽  
pp. 939-966
Author(s):  
GABRIEL LEHÉRICY
Keyword(s):  
Ordered Groups ◽  
Quasi Order ◽  
Minimal Groups

AbstractWe use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of quasi-orders some results concerning C-minimal groups given in [5].

scholarly journals Groups of height four

1980 ◽  
Vol 29 (3) ◽  
pp. 297-300 ◽  
Author(s):  
Alfred W. Hales
Keyword(s):  
Finite Index ◽  
Negative Answer ◽  
Subject Classification ◽  
Infinite Groups ◽  
Finite Height ◽  
Epimorphic Image ◽  
Quasi Order ◽  
Minimal Groups

AbstractIf G and H are infinite groups then G is said to be larger than H (H≼G) if there are subgroups A of G, B of H, each of finite index, such that B is an epimorphic image of A. Pride (1979) showed that if G has finite ‘height’ with respect to the quasi-order ≼ then there are only finitely many (classes of) minimal groups H with H ≼G, and asked whether this were true without the minimality restriction on H. This paper gives a negative answer to his question by exhibiting a group G of height four with infinitely many (classes of) groups H satisfying H≼G.1980 Mathematics subject classification (Amer. Math. Soc.): 20 E 99, 20 K 15.

Generalized Commutativity of Lattice-Ordered Groups

2015 ◽  
Vol 65 (2) ◽  
Author(s):  
M. R. Darnel ◽  
W. C. Holland ◽  
H. Pajoohesh
Keyword(s):  
Theorem Proving ◽  
Natural Generalization ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Weak Commutativity

AbstractIn this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.

Finitely generic models of TUH, for certain model companionable theories T

1985 ◽  
Vol 50 (3) ◽  
pp. 604-610
Author(s):  
Francoise Point
Keyword(s):  
Discriminator Variety ◽  
Generic Models ◽  
Elementary Class ◽  
Ordered Groups ◽  
Existentially Closed ◽  
Closed Element ◽  
Starting Point ◽  
Joint Embedding ◽  
Joint Embedding Property ◽  
Generic Elements

The starting point of this work was Saracino and Wood's description of the finitely generic abelian ordered groups [S-W].We generalize the result of Saracino and Wood to a class ∑UH of subdirect products of substructures of elements of a class ∑, which has some relationships with the discriminator variety V(∑t) generated by ∑. More precisely, let ∑ be an elementary class of L-algebras with theory T. Burris and Werner have shown that if ∑ has a model companion then the existentially closed models in the discriminator variety V(∑t) form an elementary class which they have axiomatized. In general it is not the case that the existentially closed elements of ∑UH form an elementary class. For instance, take for ∑ the class ∑0 of linearly ordered abelian groups (see [G-P]).We determine the finitely generic elements of ∑UH via the three following conditions on T:(1) There is an open L-formula which says in any element of ∑UH that the complement of equalizers do not overlap.(2) There is an existentially closed element of ∑UH which is an L-reduct of an element of V(∑t) and whose L-extensions respect the relationships between the complements of the equalizers.(3) For any models A, B of T, there exists a model C of TUH such that A and B embed in C.(Condition (3) is weaker then “T has the joint embedding property”. It is satisfied for example if every model of T has a one-element substructure. Condition (3) implies that ∑UH has the joint embedding property and therefore that the class of finitely generic elements of ∑UH is complete.)

A theorem and a question about epicomplete archimedean lattice-ordered groups

2009 ◽  
Vol 62 (2-3) ◽  
pp. 165-184 ◽  
Author(s):  
R. N. Ball ◽  
A. W. Hager ◽  
D. G. Johnson ◽  
A. Kizanis
Keyword(s):  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Archimedean Lattice

Extension of Locally Defined Indefinite Functions on Ordered Groups

2004 ◽  
Vol 50 (1) ◽  
pp. 57-81 ◽  
Author(s):  
Ram�n Bruzual ◽  
Marisela Dom�nguez
Keyword(s):  
Ordered Groups

Semigroup actions on ordered groupoids

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
Niovi Kehayopulu ◽  
Michael Tsingelis
Keyword(s):  
Commutative Semigroup ◽  
Equivalence Relation ◽  
Semigroup Actions ◽  
Ordered Groupoid ◽  
Quasi Order

AbstractIn this paper we prove that if S is a commutative semigroup acting on an ordered groupoid G, then there exists a commutative semigroup S̃ acting on the ordered groupoid G̃:=(G × S)/ρ̄ in such a way that G is embedded in G̃. Moreover, we prove that if a commutative semigroup S acts on an ordered groupoid G, and a commutative semigroup S̄ acts on an ordered groupoid Ḡ in such a way that G is embedded in S̄, then the ordered groupoid G̃ can be also embedded in Ḡ. We denote by ρ̄ the equivalence relation on G × S which is the intersection of the quasi-order ρ (on G × S) and its inverse ρ −1.

scholarly journals The general quasi-order algorithm in number theory

1986 ◽  
Vol 9 (2) ◽  
pp. 245-251 ◽  
Author(s):  
Peter Hilton ◽  
Jean Pedersen
Keyword(s):  
Number Theory ◽  
Quasi Order ◽  
Order Algorithm

This paper deals with a generalization of the Binary Quasi-Order Theorem. This generalization involves a more complicated algorithm than(0.2)t. Some remarks are made on relative merits of two dual algorithms called theψ-algorithm and theϕ-algorithm. Some illustrative examples are given.

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