A note on Hall S-permutably embedded subgroups of finite groups

• Date: 2017
• Main Author: Sinitsa, Darya
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: \(S\)-permutable subgroup; Hall \(S\)-permutably embedded subgroup; \(S\)-permutable closure; Sylow subgroup; supersoluble group; maximal subgroup; 20D10; 20D15; 20D30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/148
• Journal Title: Algebra and Discrete Mathematics

Let \(G\) be a finite group. Recall that a  subgroup \(A\) of \(G\) is said to  permute with a subgroup \(B\) if \(AB=BA\). A subgroup \(A\) of \(G\) is said to be \(S\)-quasinormal or \(S\)-permutable in \(G\)   if \(A\) permutes with all Sylow subgroups of \(G\). Recall also that \(H^{s G}\) is th...