2008/04/24 by N. I. Sandu, Nicolae Sandu, Sandu, Nicolae
Engineering · Mathematics · #20N05 #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.RA #msc:20N05
paper · pdf · doi:10.48550/arxiv.0804.3964
15 pages
arxiv created 2008/04/24 · openalex publication_date 2008/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let L be a commutative Moufang loop (CML) with multiplication group \frak M, and let \frak F(L), \frak F(\frak M) be the Frattini subgroup and Frattini subgroup of L and \frak M respectively. It is proved that \frak F(L) = L if and only if \frak F(\frak M) = \frak M and is described the structure of this CLM. Constructively it is defined the notion of normalizer for subloops in CML. Using this it is proved that if \frak F(L) ≠ L then L satisfies the normalizer condition and that any divisible subgroup of \frak M is an abelian group and serves as a direct factor for \frak M.