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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (61), 2009/

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

Authors: Natalia Lupashco

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 M of infinite commutative Moufang loop L has such an infinite subgroup A that in M every abelian subgroup which has with A an infinite intersection is a normal subgroup then the loop L is associative.

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