The Possibility of Extending Factorization Results to Infinite Abelian Groups
نویسندگان
چکیده
We shall consider three results on factoring finite abelian groups by subsets. These are the Hajós’, Rédei’s and simulation theorems. As L. Fuchs has done in the case of Hajós’ theorem we shall obtain families of infinite abelian groups to which these results cannot be extended. We shall then describe classes of infinite abelian groups for which the extension does hold. MSC 2000: 20K99 (primary); 52C22 (secondary)
منابع مشابه
Triple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کاملAddendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...
متن کامل$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings
A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...
متن کاملFactoring Certain Infinite Abelian Groups by Distorted Cyclic Subsets
We will prove that two results on factoring finite abelian groups into a product of subsets, related to Hajós’s and Rédei’s theorems, can be extended for certain infinite torsion abelian groups. Mathematics Subject Classification (2000): Primary 20K01; Secondary
متن کاملOn Quantum Algorithms for Noncommutative Hidden Subgroups
Quantum algorithms for factoring and finding discrete logarithms have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. We present a quantum algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear...
متن کامل