On dicyclic groups as inner mapping groups of finite loops

Commentationes mathematicae Universitatis Carolinae

Emma Leppälä¹ 

关键词: solvable loop;    inner mapping group;    dicyclic group;   

DOI  :  10.14712/1213-7243.2015.180

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

Let $G$ be a finite group with a dicyclic subgroup $H$. We show that if there exist $H$-connected transversals in $G$, then $G$ is a solvable group. We apply this result to loop theory and show that if the inner mapping group $I(Q)$ of a~finite loop $Q$ is dicyclic, then $Q$ is a solvable loop. We also discuss a more general solvability criterion in the case where $I(Q)$ is a certain type of a direct product.

【 授权许可】

CC BY