Finite groups whose sums of irreducible character degrees of all proper subgroups are large

Abstract

Some scholars investigated the influence of the sum of all character degrees of a finite group on group structure. In this paper, we will study the influence of sums of all character degrees of all proper subgroups of a finite group on its structure. We will show that a finite group G is solvable when all proper subgroups H of G satisfy \( T(H) ≥ \frac 2 3 |H|\), where T(H) is the sum of all character degrees of a finite group H.