On extensions of Moufang loops by a cyclic factor that is coprime to three. Issue 6 (3rd June 2017) - Drápal, Aleš
ABSTRACT: Gagola's construction of cyclic extensions of Moufang loops for orders coprime to three is investigated with the goal of describing necessary and sufficient conditions when the construction really gives a Moufang loop. This is achieved both in terms of equations and loop autotopisms. The obtained description is then specialized to Moufang loops that cyclically extend a normal subgroup G, showing the connection to Chein's construction in case when the semiautomorphism characterizing the extension is an antiautomorphism of G . These results are then illustrated upon the case when G is a noncommutative group that possesses a cyclic subgroup of index two and has a small center (i.e.| Z ( G )|∈1, 2).