Finite group with given \(c\)-permutable subgroups

• Date: 2018
• Main Author: Ahmad, Ahmad Alsheik
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: finite group; maximal subgroup; Sylow subgroup; supersoluble group; \(c\)-permutable subgroup; 20D10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/986
• Journal Title: Algebra and Discrete Mathematics

Following [1] we say that subgroups  \(H\) and \(T\) of a group \(G\) are \(c\)- permutable in \(G\) if there exists an element \(x\in G\) such that \(HT^x=T^xH\).  We prove that a finite soluble group \(G\) is supersoluble if and only if every maximal subgroup of every Sylow subgroup of \(G\) is c-...