摘要
P为群的根性,如果群的元素具有的性质P满足(a)如果x是G的P-元素,且N⊿G,那么xN是G/N的P-元素;(b)如果x∈N是N的P-元素,且N⊿G,那么x也是G的P-元素;(c)如果xN是G/N的P-元素,且N是G的正规P-子群,那么x是G的P-元素.通过群的元素具有的性质P来研究群的根性.证明了由群的元素具有的的性质P可以得到群的根性P,反之,给定由群论性质确定的群的根性R,那么存在元素的一种性质,满足(a),(b),(c),并且R-根群类R=P,其中P是P-群组成的类.还利用群的元素具有的性质所确定的群的根性研究了群的继承根性.
In this paper, the radical properties of groups by properties of elements of groups are investigated. Let P is a radical property of groups, the property P of elements of groups satisfies （a） if x is P-element of group G and N G, then xN is P-element of group G/N, （b） if x ∈ N is P-element of N and N G , then x is P- element of group G , and （c） if xN is P-element of group G/N and N is P-subgroup of G, thenx is P-element of group G. It is shown that one may obtain a radical property of groups by the property of the elements of groups. Conversely, for a radical property R determined by a group theoretical property, there is a property P of elements which satisfies the three given conditions, and that the class of R radical groups R = P , where P is the class of P-group. Finally, the radical properties of groups determined by properties of elements of groups are used to study hereditary radical properties of groups.
出处
《西南大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第6期104-107,共4页
Journal of Southwest University(Natural Science Edition)
基金
国家自然科学基金资助项目(10771180
10926129)
关键词
群的根性
群的元素的性质
群论性质
radical properties of groups
properties of elements of groups
properties of group theory
