The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs

• Date: 2016
• Main Author: Pawlik, Bartłomiej Tadeusz
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: Sylow \(p\)-subgroup; group base; wreath product of groups; Cayley graphs; 20B35; 20D20; 20E22; 05C25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/233
• Journal Title: Algebra and Discrete Mathematics

Base (minimal generating set) of the Sylow 2-subgroup of \(S_{2^n}\) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup \(P_n(2)\) of \(S_{2^n}\)  acts by conjugation on the set of all b...