Normally \(\zeta\)-reversible profinite groups

• Date: 2016
• Main Authors: Cimetta, Leone, Lucchini, Andrea
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: profinite groups; Dirichlet series; 20E07
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/137
• Journal Title: Algebra and Discrete Mathematics

We examine (finitely generated) profinite groups in which two formal Dirichlet series, the normal subgroup zeta function and the normal probabilistic zeta function, coincide; we call these groups normally \(\zeta\)-reversible. We conjecture that these groups are pronilpotent and we prove this conjec...