scholarly journals Freiman's theorem in an arbitrary abelian group

2007 ◽  
Vol 75 (1) ◽  
pp. 163-175 ◽  
Author(s):  
Ben Green ◽  
Imre Z. Ruzsa
Keyword(s):  
Abelian Group ◽  
Freiman’S Theorem ◽  
Arbitrary Abelian Group

scholarly journals Graphs on Affine and Linear Spaces and Deuber Sets

10.37236/2732 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
David S. Gunderson ◽  
Hanno Lefmann
Keyword(s):  
Abelian Group ◽  
Finite Field ◽  
Recent Work ◽  
Independent Set ◽  
Large Set ◽  
Free Graph ◽  
Linear Spaces ◽  
Ramsey’S Theorem ◽  
Positive Integers ◽  
Arbitrary Abelian Group

If $G$ is a large $K_k$-free graph, by Ramsey's theorem, a large set of vertices is independent. For graphs whose vertices are positive integers, much recent work has been done to identify what arithmetic structure is possible in an independent set. This paper addresses  similar problems: for graphs whose vertices are affine or linear spaces over a finite field,  and when the vertices of the graph are elements of an arbitrary Abelian group.

scholarly journals GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250046 ◽  
Author(s):  
YURI BAHTURIN ◽  
MATEJ BREŠAR ◽  
MIKHAIL KOCHETOV
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Vector Spaces ◽  
Closed Field ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Special Linear ◽  
Infinite Dimensional ◽  
Group Gradings ◽  
Arbitrary Abelian Group

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.

scholarly journals On the embedding problem of central cyclic extensions of abelian groups

2021 ◽  
Vol XXII C (1) ◽  
Author(s):  
Ivo Michailov ◽  
Ivaylo Dimitrov ◽  
Ivan Ivanov
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Cyclic Extension ◽  
Embedding Problem ◽  
Arbitrary Abelian Group

In this report we find the obstruction of the embedding problem related to a central cyclic extension of an arbitrary abelian group.

On Invariant Means which are Not Inverse Invariant

1968 ◽  
Vol 20 ◽  
pp. 222-224
Author(s):  
M. Rajagopalan ◽  
K. G. Witz
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Torsion Group ◽  
Invariant Mean ◽  
Invariant Means ◽  
Arbitrary Abelian Group

In (1) R. G. Douglas says: “For a finite abelian group there exists a unique invariant mean which must be inversion invariant. For an infinite torsion abelian group it is not clear what the situation is.” It is not hard to see that if every element of an abelian group G is of order 2, then every invariant mean on G is also inversion invariant (see 1, remark 4). In this note we prove the following theorem (Theorem 1 below): An abelian torsion group G has an invariant mean which is not inverse invariant if, and only if, 2G is infinite. This result, together with the theorems of Douglas, answers completely the question of the existence (on an arbitrary abelian group) of invariant means which are not inverse invariant.

scholarly journals On Unit Groups of Absolute Abelian Number Fields of Degree pq

1960 ◽  
Vol 16 ◽  
pp. 73-81
Author(s):  
Hideo Yokoi
Keyword(s):  
Abelian Group ◽  
Number Field ◽  
Unit Group ◽  
Number Fields ◽  
Free Subgroup ◽  
Finite Degree ◽  
Maximal Torsion ◽  
Torsion Free Subgroup ◽  
Torsion Free ◽  
Arbitrary Abelian Group

In this note, we denote by Q the rational number field, by EΩ the whole unit group of an arbitrary number field Ω of finite degree, and by rΩ the rank of where generally G* for an arbitrary abelian group G means a maximal torsion-free subgroup of G. (NK/ΩEK)* is shortly denoted by and (G1 : G2) is, as usual, the index of a subgroup G2 in G1.

scholarly journals Codes Closed under Arbitrary Abelian Group of Permutations

2004 ◽  
Vol 18 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Bikash Kumar Dey ◽  
B. Sundar Rajan
Keyword(s):  
Abelian Group ◽  
Arbitrary Abelian Group

scholarly journals Conditions under which a lattice is isomorphic to the subgroup lattice of an abelian group

2011 ◽  
Vol 27 (2) ◽  
pp. 193-199
Author(s):  
CAROLINA CONTIU ◽  
Keyword(s):  
Abelian Group ◽  
Normal Subgroup ◽  
Sufficient Conditions ◽  
Subgroup Lattice ◽  
Necessary And Sufficient Conditions ◽  
Arbitrary Group ◽  
Necessary And Sufficient ◽  
Arbitrary Abelian Group

In this paper, we provide necessary and sufficient conditions under which a lattice is isomorphic to the subgroup lattice of an arbitrary abelian group. We also give necessary and sufficient conditions for a lattice L, to be isomorphic to the normal subgroup lattice of an arbitrary group.

THE -CENTRE AND GRADABLE DERIVED EQUIVALENCES

2018 ◽  
Vol 105 (3) ◽  
pp. 289-315
Author(s):  
KEVIN COULEMBIER ◽  
VOLODYMYR MAZORCHUK
Keyword(s):  
Abelian Group ◽  
Tilting Modules ◽  
Derived Equivalences ◽  
Arbitrary Abelian Group

We propose a generalisation for the notion of the centre of an algebra in the setup of algebras graded by an arbitrary abelian group $G$. Our generalisation, which we call the $G$-centre, is designed to control the endomorphism category of the grading shift functors. We show that the $G$-centre is preserved by gradable derived equivalences given by tilting modules. We also discuss links with existing notions in superalgebra theory.

The Group of Extensions and Splitting Length

1974 ◽  
Vol 26 (4) ◽  
pp. 879-883 ◽  
Author(s):  
E. H. Toubassi
Keyword(s):  
Abelian Group ◽  
Positive Integer ◽  
Internal Structure ◽  
Primary Group ◽  
Arbitrary Abelian Group

This paper is concerned with the internal structure of Ext(Q, T) where Q is the group of rationals and T a reduced p-primary group of unbounded order. In [1] Irwin, Khabbaz, and Rayna define the splitting length of an arbitrary abelian group A, written l(A), to be the least positive integer n, otherwise infinity, such that A ⊗ . . . ⊗ A (n factors) splits. The concept of splitting length has been induced on Ext(Q, T), see [2; 5].

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