On subgroups of finite exponent in groups

• Datum: 2018
• 1. Verfasser: Artemovych, Orest D.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: locally finite group; finitely generated group; exponent; group of Heineken-Mohamed type; 20F50; 20F26; 20E26
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1170
• Назва журналу: Algebra and Discrete Mathematics

We investigate properties of groups with subgroups of  finite exponent and prove that  a non-perfect group  \(G\)  of infinite exponent with all proper subgroups of finite exponent has the following properties:\((1)\) \(G\) is an indecomposable  \(p\)-group,\((2)\) if the derived subgroup \(G'\...