In this paper we extend the construction of the field of rational numbers from the ring of integers to an arbitrary commutative ordered semigroup. We first construct a fractional ordered semigroup and a homomorphism ...In this paper we extend the construction of the field of rational numbers from the ring of integers to an arbitrary commutative ordered semigroup. We first construct a fractional ordered semigroup and a homomorphism φs ： R → S^-1 R. Secondly, we characterize the commutative ordered semigroup so constructed by a universal mapping property.展开更多
A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜, ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） ...A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜, ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.展开更多
A subgroup H of a finite group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜ ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜...A subgroup H of a finite group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜ ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. In this paper, we investigate the influence of s-semipermutablity of some subgroups of prime power order of a finite group on its supersolvablility.展开更多
We give a definition and some primary properties of group-valued measure with a second countable complete Boolean algebra domain, and with a subset of a first countable complete Abelian po-group codomain.
基金Supported by the Natural Science Foundation of Hubei Province in China（2004D006）
文摘In this paper we extend the construction of the field of rational numbers from the ring of integers to an arbitrary commutative ordered semigroup. We first construct a fractional ordered semigroup and a homomorphism φs ： R → S^-1 R. Secondly, we characterize the commutative ordered semigroup so constructed by a universal mapping property.
基金Supported by the NSF of China(10471085) Supported by the Shanxi Province(20051007) Supported by the Returned Chinese Students Found of Shanxi Province(Jinliuguanban [2004]7)
文摘A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜, ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.
基金NNSF of China (10471085)NSF of Shanxi Province of China (20011004)Key Proj. of Ministry of Education(02023)the Returned Overseas Students Foundation of Shanxi Province of China ([2004]7)
文摘A subgroup H of a finite group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜ ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. In this paper, we investigate the influence of s-semipermutablity of some subgroups of prime power order of a finite group on its supersolvablility.
文摘We give a definition and some primary properties of group-valued measure with a second countable complete Boolean algebra domain, and with a subset of a first countable complete Abelian po-group codomain.
