On the existence of complements in a group to some abelian normal subgroups

• Date: 2018
• Main Authors: Dixon, Martyn R., Kurdachenko, Leonid A., Otal, Javier
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Complement; splitting theorem; hierarchy of centralizers; hyperfinite group; socle of a group; socular series; section rank; 0–rank; 20E22; 20E26; 20F50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/639
• Journal Title: Algebra and Discrete Mathematics

A complement to a proper normal subgroup \(H\) of a group \(G\) is a subgroup \(K\) such that \(G=HK\) and \(H\cap K=\langle1\rangle\). Equivalently it is said that \(G \) splits over \(H\). In this paper we develop a theory that we call hierarchy of centralizers to obtain sufficient conditions for...