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

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.

MSC: 20N05

Received: 27.02.2008

Language: English

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