ON A THEOREM ABOUT THE ORDERS OF ABELIAN SUBGROUPS OF A FINITE GROUP
Li D · Journal of Southwest China Normal University · 1987
In [1], by virtue of the Graph Theory, E. A. Bsrtram obtained a theorem about the orders of Abelian subgroups of a finite group and proposed a problem. They are:Theorem 1 Let G be a finite group. Index the conjugacy classes of G according to cardinality: Let m be the smallest integer i such that . Then each Abelian subgroup A≤G has an order .problem Find necessary and sufficient conditions on G in order that equality holds in Theorem 1, for some Abelian A≤G,In this note, a brief proof of Theorem 1 is given and necessary conditions for the problem are presented.prop Let G be a finite group, A be an Abelian subgroup of G. Index the conjugacy classes of G according to cardinality: Leti be the smallest integer such that, then