On the solvability of groups of central type

Abstract

Let G G be a finite group with center Z Z 8 and irreducible complex character x x so that x ( 1 ) 2 = [ G : Z ] x{(1)^2} = [G:Z] , If the 2 2 -Sylow subgroup of G / Z G/Z has order 16 or less then G G is solvable.

In search of nonsolvable groups of central type

“…In this paper we continue the work of these authors and Isaacs [6], Gagola [4] and Yellen [14] and show' MAIN THEOREM. A nonsolvable group of central type must possess a new simple group as a composition factor.…”