Algebra Commons^™

On The Intersection Number Of Finite Groups, Humberto Bautista Serrano

Math Theses

Let G be a finite, nontrivial group. In a paper in 1994, Cohn defined the covering number of a finite group as the minimum number of nontrivial proper subgroups whose union is equal to the whole group. This concept has received considerable attention lately, mainly due to the importance of recent discoveries. In this thesis we study a dual concept to the covering number. We define the intersection number of a finite group as the minimum number of maximal subgroups whose intersection is equal to the Frattini subgroup. Similarly we define the inconjugate intersection number of a finite group as …