Moufang semidirect products of loops with groups and inverse property extensions

Commentationes mathematicae Universitatis Carolinae

Mark Greer¹ 

关键词: extensions;    semidirect products;    Moufang loops;    inverse property loops;   

DOI  :  

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 】

We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S.~Gagola III, {\it Cyclic extensions of Moufang loops induced by semiautomorphisms\/}, J. Algebra Appl. {\bf 13} (2014), no.~4, 1350128], but from an external point of view.

【 授权许可】

CC BY