| Conţinutul numărului revistei |
| Articolul precedent |
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 SM ISO690:2012SANDU, Nicolae. On Frattini subloops and normalizers of commutative Moufang loops. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2012, nr. 3(70), pp. 16-27. ISSN 1024-7696. |
| EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
 Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica |
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| Numărul 3(70) / 2012 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 16-27 | ||||||
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 Descarcă PDF |
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Let L be a commutative Moufang loop (CML) with the multiplication group M, and let F(L), F(M) be the Frattini subloop of L and Frattini subgroup of M. It is proved that F(L) = L if and only if F(M) = M, and the structure of this CML is described. The notion of normalizer for subloops in CML is defined constructively. Using this it is proved that if F(L) 6= L, then L satisfies the normalizer condition and that any divisible subgroup of M is an abelian group and serves as a direct factor for M. |
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| Cuvinte-cheie Commutative Moufang loop, multiplication group, Frattini subloop, Frattini subgroup |
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