6533b7dbfe1ef96bd127092e

RESEARCH PRODUCT

Homomorphs and wreath product extensions

Peter Förster

subject

Class (set theory)PermutationPure mathematicsWreath productGeneral MathematicsSylow theoremsRepresentation (systemics)Abelian groupMathematics

description

A homomorph is a class of (finite soluble) groups closed under the operation Q of taking epimorphic images. (All groups considered in this paper are finite and soluble.) Among those types of homomorphs that have found particular interest in the theory of finite soluble groups are formations and Schunck classes; the reader is referred to (2), § 2, for a definition of those classes. In the present paper we are interested in homomorphs satisfying the following additional closure property:(W0) if A is abelian with elementary Sylow subgroups, then each wreath product A G (with respect to an arbitrary permutation representation of G) with G ∊ is contained in .

https://doi.org/10.1017/s0305004100059739