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On commutative Moufang loops with some restrictions for subgroups of its multiplication groups.
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.
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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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Contents
- Quotient rings of pseudonormed rings.
- Numerical treatment of the Kendall equation in the analysis of priority queueing systems.
- On the Division of Abstract Manifolds in Cubes.
- The numerical analysis of the tense condition of a solid body with the asymmetrical tensor of strains.
- On the coproducts of cyclics in commutative modular and semisimple group rings.
- Commutative Moufang loops with maximum conditions for subloops.
- Discontinuous term of the distribution for Markovian random evolution in R3.
- On an algebraic method in the study of integral equations with shift.
- On a family of Hamiltonian cubic planar differential systems.
- The solvability and properties of solutions of an integral convolutional equation.
- On commutative Moufang loops with some restrictions for subgroups of its multiplication groups.
- The property of universality for some monoid algebras over non-commutative rings.
- Junior spatial groups of (22'1)-symmetry.
