The Influence Of The Cover-avoiding Property On The Structure Of Finite Groups

In the investigation process of finite group subgroup and Sylow subgroup maxi-mal subgroup structure has a very important impact on the group.Many group theory scholars made fruitful work around these aspects,got a lot of meaningful results.This dissertation as this aspect research,starting from the cover away from the nature of subgroup integrated with the group of class structure.In this paper,we give the gener-alized covering distance property of some new subgroups,and by means of objects such as the Sylow subgroup,the maximal subgroup of the Sylow subgroup,the maximal sub-group,the p-solvable group,the p-module group,and the generalized p-supersolvable group class(?)p#={G|H/K≤D(G/K)or H/K is p-group or |H/K|p=p},and on this basis we define new generalized p-soluble group class(?)p*={G|H/K is p’-group or H/K is p-group or |H/K|p=p} a series of research,get some new characterizations about them.The results about p-supersolvable group is:G is a finite group,p is a,prime factor of |G|.G is a p-supersolvable group if and only if every Sylow p-subgroup of G is a CAPu-subgroup in G.Result is about general p-soluble group:group G is a generalized p-solvable when and only when a group of every Sylow p-subgroup in group G has a generalized p-solvable CAP-subgroup.About p-supersolvable group and p-mold group as a result of:If a group of any great Sylow p-subgroup of G is CAP-subgroup,then G is a p-supersolvable group G=Op(G).The full text is divided into three chapters:The first chapter is introduction.Mainly introduced in this paper,some related background and existing research results;The second chapter is the preliminary knowledge,mainly gives the related concepts and the main lemma;The third chapter is to study the related structures of generalized p-supersolvable group,p-supersolvable group,p-module group,p-solvable group,generalized p-solvable group,p-supersolvable group and generalized p-supersolvable group by using gener-alized covering remobilities in combination with the covering remobilities of Sylow subgroups...