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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2009, Number 3, Pages 52–56 (Mi basm236)  

Research articles

On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups

Natalia Lupashco

Tiraspol State University, Departament of Mathematics, Chişinău, Moldova
References:
Abstract: It is proved that if an infinite commutative Moufang loop $L$ has such an infinite subloop $H$ that in $L$ every associative subloop which has with $H$ an infinite intersection is a normal subloop then the loop $L$ is associative. It is also proved that if the multiplication group $\mathfrak M$ of infinite commutative Moufang loop $L$ has such an infinite subgroup $\mathfrak N$ that in $\mathfrak M$ every abelian subgroup which has with $\mathfrak N$ an infinite intersection is a normal subgroup then the loop $L$ is associative.
Keywords and phrases: commutative Moufang loop, multiplication group, infinite associative subloop, infinite abelian subgroup.
Received: 27.02.2008
Bibliographic databases:
Document Type: Article
MSC: 20N05
Language: English
Citation: Natalia Lupashco, “On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, no. 3, 52–56
Citation in format AMSBIB
\Bibitem{Lup09}
\by Natalia~Lupashco
\paper On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2009
\issue 3
\pages 52--56
\mathnet{http://mi.mathnet.ru/basm236}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2643154}
\zmath{https://zbmath.org/?q=an:1189.20064}
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