6533b7dbfe1ef96bd127092e
RESEARCH PRODUCT
Homomorphs and wreath product extensions
Peter Förstersubject
Class (set theory)PermutationPure mathematicsWreath productGeneral MathematicsSylow theoremsRepresentation (systemics)Abelian groupMathematicsdescription
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 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1982-07-01 | Mathematical Proceedings of the Cambridge Philosophical Society |