Serial group rings of finite groups. \(p\)-solvability

• Date: 2018
• Main Authors: Kukharev, Andrei, Puninski, Gena
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Serial ring; group ring; \(p\)-solvable group; 20C05,16L30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1157
• Journal Title: Algebra and Discrete Mathematics

We prove that for any finite \(p\)-solvable group \(G\) with a cyclic \(p\)-Sylow subgroup and any field \(F\) of characteristic \(p\), the group ring \(FG\) is serial. As a corollary for an arbitrary field we will produce a list of all groups of order \(\leq 100\) whose group rings are serial.