纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
5期
491-495
,共5页
有限群%B 群%有限p群
有限群%B 群%有限p群
유한군%B 군%유한p군
finite groups%B groups%finite p groups
主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群，即B 群.B群是全可置换群的扩展，利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B 群的结构进行一些刻画.应用B 群的结构得到有限p (p>2)群为二元生成的B 群的充要条件.
主要研究子群置換性質對有限群結構的影響.通過子群的置換性得到一類群，即B 群.B群是全可置換群的擴展，利用全可置換群的p次中心擴張和子群的階得到B群的一些性質併對B 群的結構進行一些刻畫.應用B 群的結構得到有限p (p>2)群為二元生成的B 群的充要條件.
주요연구자군치환성질대유한군결구적영향.통과자군적치환성득도일류군，즉B 군.B군시전가치환군적확전，이용전가치환군적p차중심확장화자군적계득도B군적일사성질병대B 군적결구진행일사각화.응용B 군적결구득도유한p (p>2)군위이원생성적B 군적충요조건.
The paper studies the influence of subgroups replacement properties on the structure of finite groups. A finite group is derived from the subgroup replacement properties, which is called B group. B groups is the extension of full permutation groups, the power of p center expansion of full permutation groups and Subgroups order use to get some properties of B groups and descriptions about the structure of B groups. By using the structure of B group, we get the necessary and sufficient conditions of a finite p (p> 2) group being a binary generating B group.
