Simple Moufang loops and Galois extensions

Abstract

The paper establishes an one-to-one correspondence between simple Moufang loops and Paige loops constructed over Galois extension over prime field in its algebraic closure. Using this connection it describes fully the family of nonassociative finite simple Moufang loops.It describes the generators, the loop structure of subloops, the automorphism group of nonassociative simple Moufang loops.

14 pages

References in corpus (2)

• About the embedding of Moufang loops in alternative algebras
• The classification on simple Moufang loops

Cited by in corpus (1)

• Radicals and embeddings of Moufang loops in alternative loop algebras