Sylow's theorem for Moufang loops

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion of the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow subloops.Comment: 21 page

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP, Brazil[Proc.04/07181-1]CNPq, BrazilConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS)FAPERGS, Brazil[Proc.03/0516-2]RFBR[05-01-00797]RFBRSB RAS, Russia[29]SB RAS, RussiaSB RAS, RussiaSB RAS, Russia[2006.1.2