有限群的結(jié)構(gòu)與次覆蓋遠(yuǎn)離性.pdf

1、南昌大學(xué)碩士學(xué)位論文有限群的結(jié)構(gòu)與次覆蓋遠(yuǎn)離性姓名：彭康泰申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：王燕鳴李樣明20081020AbstractABSTRACTInthispaper，wegivethesub—coveravoidancepropertyinafinitegroupLetGbeafinitegroupandHasubgroupofGHissaidtOhavethesub—coveravoidancepropertyinG

2、ifthereisachiefseries1=GoGlGI=GofGsuchthatforeveryi=1，，Z，Gf—l(HnG，)qqGInthispaper，wegivesomenecessaryandsufficientconditionsofafinitegrouptobesolvableundertheassumptionsthatsomesubgroupsofafinitegroupsatisfiesthesub—cove

3、ravoidancepropertyThemainresultsareasfollows：Theorem33LetGbeafinitegroupThenthefollowingstatementsareequivalent：(1)Gissolvable；(2)EverysubgroupofGhasthesubcoveravoidinginG：(3)EverymaximalsubgroupofGhasthesub—coveravoidin

4、ginG：(4)EveryHallsubgroupofGhasthesubcoveravoidinginG；(5)EverySylowsubgroupofGhasthesub—coveravoidinginG：(6)ThereisaSylowsubgroupPofGforeveryP∈刀(G)suchthatPhasthesubcoveravoidancepropertyinG；∽ThereisaSylowsubgroupPofGfor

5、everyP∈刀(G)suchthatPhasthePsubcoveravoidancepropertyinGTheorem35LetGbeafinitegroupandp∈萬(G)IfPsmin：r(Soc(G))Or0—1，IGl)：1，thenthefoUowingstatementsareequivalent：(1)GisP—solvable；(2)EverymaximalsubgroupofeachSylowsubgroupo

6、fGhasthesubcoveravoidancepropertyinG；(3)ThereisaSylowsubgroupPofGsuchthateverymaximalsubgroupofPhasthesub—coveravoidancepropertyinG；(4)ThereisaSylowsubgroupPofGsuchthatPcontainsamaximalsubgrouphavingtheP—subcoveravoidanc