Several Normality Conditions Of Subgroup And The Structure Of The Group

Using some kind of normality conditions of subgroup to study the structure of finitegroup has been limited group of study important issue. For a long time, group theory scholarsused all kinds of generalized normality to depict the structure of finite group, got a lot ofresults. On these bases, this paper further weakens the group of normality conditions forNS quasinormal, so as to get new normality and the relationship between the structures ofthe group.Full text main content is divided into the following four chapters:The first chapter mainly introduces the application of subgroup normality conditionsresearch group of the structure of the background and present situation.The second chapter, this paper introduces some studies of finite group basic knowledge.In the third chapter, this paper introduces the main research contents during my studenttime, such as in quasinormal subgroup, S quasinormal subgroup, quasinormal embeddedsubgroup conditions how to study the structure and properties of the finite group.The fourth chapter, we found that if G is finite group, H G, if every primeptomeet (p, H)1, and H K Gfor each K,N K H all have contains some Sylow p subgroup of. This subgroup have significant new idea, the life as a quasinormalsubgroup, then also proved quasinormal subgroup meet subgroup genetic and quotientgroup genetic, and apply it to get the limited group of super solvability of some importantconclusion.