A new characterization of finite \(\sigma\)-soluble \(P\sigma T\)-groups

• Date: 2020
• Main Author: Adarchenko, N. M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: finite group; \(\sigma\)-permutable subgroup; \(P\sigma T\)-group; \(\sigma\)-soluble group; \(\sigma\)-nilpotent group; 20D10; 20D15; 20D30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1530
• Journal Title: Algebra and Discrete Mathematics

Let \(\sigma =\{\sigma_{i} \mid i\in I\}\) be a partition of the set of all primes \(\mathbb{P}\) and \(G\) a finite group. \(G\) is said to be \emph{\(\sigma\)-soluble} if every chief factor \(H/K\) of \(G\) is a \(\sigma_{i}\)-group for some \(i=i(H/K)\). A set \({\mathcal H}\) of subgroups of \(G...