有限群的π-闭-sylow塔-s-补(Ⅰ)  

On π-close - Sylow - tower - s - supplemented Subgroups of Finite Groups

作　　者：於遒[1] 翟余华 李科生[1] 张新建[2] 

机构地区：[1]淮海工学院东港学院,江苏连云港222069 [2]淮阴师范学院数学系,江苏淮安223001

出　　处：《淮阴工学院学报》2003年第5期1-3,共3页Journal of Huaiyin Institute of Technology

基　　金：淮海工学院自然基金(03-1-41)

摘　　要：称群G的子群H在G中π-闭-sylow塔-s-可补的,如果存在G的子群K,使得G=HK且K/K∩H_G为π-sy-low塔群,此时,K被称为H在群G中的π-闭-sylow塔-s-补。讨论了π-闭-sylow塔群的性质并应用这些性质给出了一个群π-sylow塔-s-补的一些结论。主要结论有:设G为群,H为群G的子群,则下列论断成立:(1)如果K是H在G中的π-闭-sylow塔-s-补,且NG,则KN/N为HN/N在G/N中的π-闭-sylow塔-s-补;(2)令NC且N<H,若K/N是H/N在G/N中的π-闭-sylow塔-s-补,则K为H在G中的π-闭-sylow塔-s-补;(3)如果H≤T≤G,并且K是H在G中的π-闭-sylow塔-s-补,那么K∩T为H在T中的π-闭-sylow塔-s-补。A subgroup H is called p - close - Sylow - tower - s - supplemented in group G if there exists subgroup K of G such that HK = G and K/K ∩ HG is a p - close - Sylow tower group. Some properties about p -close - sylow - tower - s - supplemented are obtained as follows through the use of the characters of p - close -Sylow - tower groups: Let G be a group and H a subgroup of G, then (1) If K is a p- close - Sylow tower subgroup of H in G and N G, then KN/N is a p - close - sylow tower subgroup of HN/N in G/N; (2) N G and N≤H, then K/N is a p - close - Sylow tower subgroup of H/N in G/N if and only if K is a p - close - Sylow tower subgroup of H in G;(3) If H≤T≤G and K is a p -close -Sylow tower subgroup of H in G, then K∩T is a p - close - Sylow tower subgroup of H in T.

关 键 词：有限群 Π-闭-SYLOW塔群 π-闭-sylow塔-s-补 称群 子群 

分 类 号：O152.1[理学—数学]