It seems that we can decompose permutation groups to wreath product of primitive permutations, much in the same way that abstract groups are decomposed to semi-direct product of simple groups.
However, I have a hard time finding a basic reference explaining this in more detail in a simple language.
Can you suggest some references for a beginner?
Here are the sort of questions I need answered by a reference:
- Are there other decompositions for permutaion groups?
- An intuitive explanation of primitive wreath product.
- The relation between the decomposition of abstract and permutation groups (if any)
One relevant online resource I could find is this paper, but only the early part of the paper seems basic and relevant.
I also have access to the Dixon and Mortimer's "Permutation Groups", but I couldn't find explicit discussion of these dicomposition ideas in that book.