Abstract:This paper completely solves the isomorphism problem for Moufang loops $Q = GC$ where $G\unlhd Q$ is a noncommutative group with cyclic subgroup of index two and $|Z(G)| \le 2$, $C$ is cyclic, $G\cap C = 1$, and $Q$ is finite of order coprime to three.
Keywords: dihedral group; Moufang loop; cyclic extension; semidirect product
DOI: DOI 10.14712/1213-7243.2015.187
AMS Subject Classification: 20N05