Relatively thin and sparse subsets of groups

• Date: 2011
• Main Authors: Lutsenko, Ie., Protasov, I. V., Луценко, І., Протасов, І. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2712
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $G$ be a group with identity $e$ and let $\mathcal{I}$ be a left-invariant ideal in the Boolean algebra $\mathcal{P}_G$ of all subsets of $G$. A subset $A$ of $G$ is called $\mathcal{I}$-thin if $gA \bigcap A \in \mathcal{I}$ for every $g \in G \ \{e\}$. A subset $A$ of $G$ is called $\mathcal{I...