ON THE SOLVABILITY OF A FINITE GROUP BY THE SUM OF SUBGROUP ORDERS

摘要

Let G be a finite group and σ1(G) = 1 |G| P H≤G |H|.Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of G, we prove that if σ1(G) < 117 20 , then G is solvable.This partially solves an open problem posed in [9].