论文标题
无限的联合最小对涉及腔序列和概括更高维度
Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions
论文作者
论文摘要
Nathanson启动了一组或半群中最小补充的研究。最小补充和最小补充的概念导致了共同最小对的概念，这在作者先前的工作中被考虑。在本文中，我们研究了整数中哪种类型的子集和较高等级的自由阿伯利亚群体可以成为共同最小对的一部分。我们表明，大多数腔序列具有此属性。从建立的条件来看，可以表明，任何有限生成的阿伯利亚群的任何无限子集都具有无数的子集，这是共同对的一部分。此外，可以选择无数集合的集合，以便满足某些代数属性。
The study of minimal complements in a group or a semigroup was initiated by Nathanson. The notion of minimal complements and being a minimal complement leads to the notion of co-minimal pairs which was considered in a prior work of the authors. In this article, we study which type of subsets in the integers and free abelian groups of higher rank can be a part of a co-minimal pair. We show that a majority of lacunary sequences have this property. From the conditions established, one can show that any infinite subset of any finitely generated abelian group has uncountably many subsets which is a part of a co-minimal pair. Further, the uncountable collection of sets can be chosen so that they satisfy certain algebraic properties.
