Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups

• Date: 2018
• Main Authors: Slupik, Anna J., Sushchansky, Vitaly I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Cayley graph; Sylow \(p\)-subgroup; Frattini subgroup; 20B35; 05C25; 05C12; 20F65
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803
• Journal Title: Algebra and Discrete Mathematics

Minimal generating sets of a Sylow \(p\)-subgroup \(P_n\) of the symmetric group \(S_{p^n}\) are characterized. The number of ordered minimal generating sets of \(P_n\) is calculated. The notion of the type of a generating set of \(P_n\) is introduced and it is proved that \(P_n\) contains minimal g...