Authors: N.T. Lupashco
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.
– 0.11 Mb
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.
Fulltext
– 0.11 Mb
