CYCLIC EXTENSIONS OF MOUFANG LOOPS INDUCED BY SEMI-AUTOMORPHISMS

Abstrakt

It is well-known that if a group G factorizes as G = NH where H {= G and N (sic) G then the group structure of G is determined by the subgroups H and N, the intersection N boolean AND H and how H acts on N with a homomorphism phi : H -> Aut(N). Here, we generalize the idea by creating extensions using the semi-automorphism group of N.

We show that if G = NH is a Moufang loop, N is a normal subloop, and H = is a finite cyclic group of order coprime to three then the binary operation of G depends only on the binary operation of N, the intersection N boolean AND H, and how u permutes the elements of N as a semi-automorphism of N.

Klíčová slova

• Group extension
• semidirect product
• semi-automorphism
• Moufang loop