ON GROUPS OF CENTRAL TYPE

Abstract

This chapter reviews groups of central type. K. Iwahori and S. Matsumoto noted that G, a finite group with center Z having an irreducible character x such that x(1)2 = [G:Z], is a group of central type if and only if there is a central simple projective group algebra KH associated with G where H is finite. They conjectured that groups of central type are solvable. G/Z, where G is a counterexample to the conjecture, has a homomorpnic image, say G/N, such that S1 × … × Sm ≤ G/N ≤ Aut(S1 × … × Sm), where Si ≅ S a non-Abelian simple group and G/N acts transitively on the m components.