Authors: N.T. Lupashco
Abstract
Let

be the multiplication group of a commutative Moufang loop Q. In this paper it is proved that if all infinite abelian subgroups of

are normal in

, then Q is associative. If all infinite nonabelian subgroups of

are normal in

, then all nonassociative subloops of Q are normal in Q, all nonabelian subgroups of

are normal in

and the commutator subgroup

is a finite 3-group.
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