Wreath products and Fitting classes of $\mathfrak S_1$-groups

Abstract

It is a well known result of Blessenohl and Gaschütz that the corresponding concepts coincide for finite soluble groups. Here we consider the wreath product property (wpp) : X satisfies wpp if whenever G E X and p is a prime, there is an integer n such that G' 2 Cp E X. An abelian normal Fitting class satisfies wpp but a nonabelian normal Fitting class may not. Embedding theorems related te those of Blessenohl and Gaschiltz show further distinctions between abelian and nonabelian normal Fitting classes. For example, if X is an abelian normal Fitting class, then s-T = 61 ; this is false for nonabelian normal Fitting classes. 10. D .J .S. ROBINSON, "Finiteness conditions and generalized soluble groups," (2 vols),