<?xml version='1.0' encoding='utf-8'?>
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<creators>
<creator>
<creatorName>Sandu, N.</creatorName>
<affiliation>Universitatea de Stat din Tiraspol, Moldova, Republica</affiliation>
</creator>
</creators>
<titles>
<title xml:lang='en'>On Frattini subloops and normalizers of commutative Moufang loops</title>
</titles>
<publisher>Instrumentul Bibliometric National</publisher>
<publicationYear>2012</publicationYear>
<relatedIdentifier relatedIdentifierType='ISSN' relationType='IsPartOf'>1024-7696</relatedIdentifier>
<subjects>
<subject>Commutative Moufang loop</subject>
<subject>multiplication group</subject>
<subject>Frattini
subloop</subject>
<subject>Frattini subgroup</subject>
</subjects>
<dates>
<date dateType='Issued'>2012-06-01</date>
</dates>
<resourceType resourceTypeGeneral='Text'>Journal article</resourceType>
<descriptions>
<description xml:lang='en' descriptionType='Abstract'>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.</description>
</descriptions>
<formats>
<format>application/pdf</format>
</formats>
</resource>