Theta Subgroups and the Solvability of FiniteGroups  

作　　者：李秀玲 赵耀庆 

机构地区：[1]Department [2]of

出　　处：《Chinese Quarterly Journal of Mathematics》1998年第3期36-42, ,共7页数学季刊（英文版）

基　　金：.NULL.

摘　　要：For a maximal subgroup M of a finite group G ,a θ subgroup for M is any subgroup C of G such that CM and Core G(M∩C) is maximal among normal subgroups of G properly contained in C . This concept is motivated by the concept of θ pairs which was introduced by N .P.Mukherjee and P.Bhattacharya. The present paper represents an attempt to carry the studies on θ pairs further.We study intrinsic properties of a given family of maximal subgroups and its associate θ subgroups which imply a group to be solvable, π solvable and supersolvable. All of these results are effective improvements of known relative results on θ pairs.For a maximal subgroup M of a finite group G ,a θ subgroup for M is any subgroup C of G such that CM and Core G(M∩C) is maximal among normal subgroups of G properly contained in C . This concept is motivated by the concept of θ pairs which was introduced by N .P.Mukherjee and P.Bhattacharya. The present paper represents an attempt to carry the studies on θ pairs further.We study intrinsic properties of a given family of maximal subgroups and its associate θ subgroups which imply a group to be solvable, π solvable and supersolvable. All of these results are effective improvements of known relative results on θ pairs.

关 键 词：有限群 θ-子群 可解性 

分 类 号：O152.1[理学—数学]