On extensions of Moufang loops by a cyclic factor that is coprime to three

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 obtain...

Full description

Saved in:
Bibliographic Details
Published in:Communications in algebra 2017-06, Vol.45 (6), p.2350-2376
Main Author: Drapal, Ales
Format: Article
Language:English
Subjects:
Algebra
Cyclic extension
Joints
Mathematical analysis
Moufang loop
semiautomorphism
semidirect product
Subgroups
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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}).
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2016.1233202