Abstract: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.
Keywords: extensions; semidirect products; Moufang loops; inverse property loops
AMS Subject Classification: 20N05