Groups with many generalized \(FC\)-subgroup

• Date: 2018
• Main Authors: Russo, Alessio, Vincenzi, Giovanni
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Conjugacy class; \(FC\)-groups; normalizer subgroup; subnormal subgroup; 20F24
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/802
• Journal Title: Algebra and Discrete Mathematics

Let \(FC^0\) be the class of all finite groups, and for each non-negative integer \(m\) define by induction the group class \(FC^{m+1}\) consisting of all groups \(G\) such that the factor group \(G/C_G(x^G)\) has the property \(FC^m\) for all elements \(x\) of \(G\). Clearly, \(FC^1\) is the class...