On extensions of Moufang loops by a cyclic factor that is coprime to three. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Drápal, Aleš
• Is Part Of: Communications in algebra. Volume 45:Issue 6(2017)
• Page Start: 2350
• Page End: 2376
• Publication Date: 2017-06-03
• Subjects: Cyclic extension -- Moufang loop -- semiautomorphism -- semidirect product; 20N05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1233202
• Languages: English
• ISSNs: 0092-7872

Abstract

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}).