On multilattice groups. II

1966 ◽  
Vol 62 (2) ◽  
pp. 149-164 ◽  
Author(s):  
D. B. Mcalister
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Positive Element ◽  
Necessary And Sufficient Conditions ◽  
Countable Number ◽  
Direct Sums ◽  
Lattice Group ◽  
Ordered Groups ◽  
Group A ◽  
Necessary And Sufficient

Conrad ((2)), has shown that any lattice group which obeys (C.F.) each strictly positive element exceeds at most a finite number of pairwise orthogonal elements may be constructed, from a family of simply ordered groups, by carrying out, alternately, the operations of forming finite direct sums and lexico extensions, at most a countable number of times. The main result of this paper, Theorem 3.1, gives necessary and sufficient conditions for a multilattice group, which obeys (ℋ*), to be isomorphic to a multilattice group which is constructed from a family of almost ordered groups, by carrying out, alternately, the operations of forming arbitrary direct sums and lexico extensions, any number of times; we call such a group a lexico sum of the almost ordered groups.

scholarly journals Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Brendan Goldsmith ◽  
Ketao Gong
Keyword(s):  
Abelian Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Direct Sums ◽  
Direct Sum ◽  
Zero Entropy ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions to ensure that the direct sum of two Abelian groups with zero entropy is again of zero entropy are still unknown; interestingly the same problem is also unresolved for direct sums of Hopfian and co-Hopfian groups.We obtain sufficient conditions in some situations by placing restrictions on the homomorphisms between the groups. There are clear similarities between the various cases but there is not a simple duality involved.

Groups with prescribed automorphism group: A clarification

1984 ◽  
Vol 27 (1) ◽  
pp. 59-60
Author(s):  
Derek J. S. Robinson
Keyword(s):  
Automorphism Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group A ◽  
Necessary And Sufficient ◽  
Central Automorphisms ◽  
Semisimple Subgroup

In Theorems 1 and 2 of [] necessary and sufficient conditions were given for a group G to have a finite automorphism group Aut G and a semisimple subgroup of central automorphisms AutcG. Recently it occurred to us, as a result of conversations with Ursula Webb, that these conditions could be stated in a much simpler and clearer form. Our purpose here is to record this reformulation. For an explanation ofterminology and notation we refer the reader to [1].

scholarly journals Pointwise stabilization of the Poisson integral for the diffusion type equations with inertia

2016 ◽  
Vol 8 (2) ◽  
pp. 279-283
Author(s):  
H.P. Malytska ◽  
I.V. Burtnyak
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Poisson Integral ◽  
Diffusion Type ◽  
Necessary And Sufficient ◽  
Parabolic Degeneracy

In this paper we consider the pointwise stabilization of the Poisson integral for the diffusion type equations with inertia in the case of finite number of parabolic degeneracy groups. We establish necessary and sufficient conditions of this stabilization for a class of bounded measurable initial functions.

scholarly journals On automorphisms of finite Abelian p-groups

2008 ◽  
Vol 58 (4) ◽  
Author(s):  
Marek Golasiński ◽  
Daciberg Gonçalves
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finitely Generated ◽  
Type K ◽  
Group A ◽  
Necessary And Sufficient ◽  
Torsion Part

AbstractLet A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A p.For a finite abelian p-group A of type (k 1, ..., k n), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k 1, k 2) is analyzed.

scholarly journals A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2897-2905
Author(s):  
Omid Zabeti
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lattice Structures ◽  
Fatou Property ◽  
Topological Structures ◽  
Lattice Group ◽  
Topological Lattice ◽  
Bounded Group ◽  
Different Types ◽  
Necessary And Sufficient

Suppose G is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on G which have topological structures. In this paper, our attempt is to assign lattice structures on them. More precisely, we use of a version of the remarkable Riesz-Kantorovich formulae and Fatou property for bounded order bounded homomorphisms to allocate the desired structures. Moreover, we show that unbounded convergence on a locally solid lattice group is topological and we investigate some applications of it. Also, some necessary and sufficient conditions for completeness of different types of bounded group homomorphisms between topological rings have been obtained, as well.

A Note on Quadratic Forms and the u-invariant

1974 ◽  
Vol 26 (5) ◽  
pp. 1242-1244 ◽  
Author(s):  
Roger Ware
Keyword(s):  
Finite Number ◽  
Quadratic Forms ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Real Field ◽  
Witt Ring ◽  
Necessary And Sufficient

The u-invariant of a field F, u = u(F), is defined to be the maximum of the dimensions of anisotropic quadratic forms over F. If F is a non-formally real field with a finite number q of square classes then it is known that u ≦ q. The purpose of this note is to give some necessary and sufficient conditions for equality in terms of the structure of the Witt ring of F.

The Brascamp–Lieb Polyhedron

2010 ◽  
Vol 62 (4) ◽  
pp. 870-888 ◽  
Author(s):  
Stefán Ingi Valdimarsson
Keyword(s):  
Finite Number ◽  
Related Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Maps ◽  
Rank 2 ◽  
Necessary And Sufficient ◽  
Concise Description

AbstractA set of necessary and sufficient conditions for the Brascamp–Lieb inequality to hold has recently been found by Bennett, Carbery, Christ, and Tao. We present an analysis of these conditions. This analysis allows us to give a concise description of the set where the inequality holds in the case where each of the linear maps involved has co-rank 1. This complements the result of Barthe concerning the case where the linear maps all have rank 1. Pushing our analysis further, we describe the case where the maps have either rank 1 or rank 2.A separate but related problem is to give a list of the finite number of conditions necessary and sufficient for the Brascamp–Lieb inequality to hold. We present an algorithm which generates such a list.

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