On Frattini subloops and normalizers of commutative Moufang loops
| dc.creator | Sandu, Nicolae | |
| dc.date | 2008-04-24 | |
| dc.date.accessioned | 2026-07-07T09:35:02Z | |
| dc.date.available | 2026-07-07T09:35:02Z | |
| dc.description | 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 $\frak F(L) \neq L$ 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.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0804.3964 | |
| dc.identifier | http://arxiv.org/abs/0804.3964 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159702 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 20N05 | |
| dc.title | On Frattini subloops and normalizers of commutative Moufang loops | |
| dc.type | text |