Mathematics – Group Theory
Scientific paper
2003-12-18
Mathematics
Group Theory
25 pages
Scientific paper
A permutation group is innately transitive if it has a transitive minimal normal subgroup, which is referred to as a plinth. We study the class of finite, innately transitive permutation groups that can be embedded into wreath products in product action. This investigation is carried out by observing that such a wreath product preserves a natural Cartesian decomposition of the underlying set. Previously we classified the possible embeddings in the case where the plinth is simple. Here we extend that classification and identify several different types of Cartesian decompositions that can be preserved by an innately transitive group with a non-abelian plinth. These different types of decompositions lead to different types of embeddings of the acting group into wreath products in product action. We also obtain a full characterisation of embeddings of innately transitive groups with diagonal type into such wreath products.
Baddeley Robert W.
Praeger Cheryl E.
Schneider Csaba
No associations
LandOfFree
Innately transitive subgroups of wreath products in product action does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Innately transitive subgroups of wreath products in product action, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Innately transitive subgroups of wreath products in product action will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-308448