Groups containing locally maximal product-free sets of size 4

• Date: 2021
• Main Author: Anabanti, C. S.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2021
• Subjects: product-free sets; locally maximal; maximal; groups; 20D60; 05E15; 11B75
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1347
• Journal Title: Algebra and Discrete Mathematics

Every locally maximal product-free set \(S\) in a finite group \(G\) satisfies \(G=S\cup SS \cup S^{-1}S \cup SS^{-1}\cup \sqrt{S}\), where \(SS=\{xy\mid x,y\in S\}\), \(S^{-1}S=\{x^{-1}y\mid x,y\in S\}\), \(SS^{-1}=\{xy^{-1}\mid x,y\in S\}\) and \(\sqrt{S}=\{x\in G\mid x^2\in S\}\). To better under...