On Frattini subloops and normalizers of commutative Moufang loops

dc.creatorSandu, Nicolae
dc.date2008-04-24
dc.date.accessioned2026-07-07T09:35:02Z
dc.date.available2026-07-07T09:35:02Z
dc.descriptionLet $L$ 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 $\frak F(L) \neq L$ 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 $\frak M$.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0804.3964
dc.identifierhttp://arxiv.org/abs/0804.3964
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159702
dc.subjectRings and Algebras
dc.subject20N05
dc.titleOn Frattini subloops and normalizers of commutative Moufang loops
dc.typetext

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