J. Aust. Math. Soc.
77 (2004), 55-72
|
Transitive simple subgroups of wreath products in product action
|
|
|
Abstract
|
A transitive simple subgroup of a finite
symmetric group is very rarely contained in a
full wreath product in product action. All such
simple permutation groups are determined in this
paper. This remarkable conclusion is reached
after a definition and detailed examination of
`Cartesian decompositions' of the permuted set,
relating them to certain `Cartesian systems of
subgroups'. These concepts, and the bijective
connections between them, are explored in greater
generality, with specific future applications in
mind.
|
Download the article in PDF format (size 172 Kb)
|
|
|
|