It is known that the product of two nilpotent subgroups of a finite group is not necessarily nilpotent.In this paper, we study the influence of the Engel condition on the product of two nilpotent subgroups. Ou...It is known that the product of two nilpotent subgroups of a finite group is not necessarily nilpotent.In this paper, we study the influence of the Engel condition on the product of two nilpotent subgroups. Our results generalize some well-known results.展开更多
Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nil...Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.展开更多
基金Supported by the Nitional Science Foundation of China !(19871073)
文摘It is known that the product of two nilpotent subgroups of a finite group is not necessarily nilpotent.In this paper, we study the influence of the Engel condition on the product of two nilpotent subgroups. Our results generalize some well-known results.
文摘Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.
