TITLE: What version of the wreath product embedding theorem is actually stated in the famous paper of Kaloujnine and Krasner?
QUESTION [6 upvotes]: This question is inspired by Terry Tao's blog post and the comments there.  I have always cited M. Krasner and L. Kaloujnine, "Produit complet des groupes de permutations et le problème d'extension de groupes III", Acta Sci. Math. Szeged 14, pp. 69-82 (1951) as the source of the result that if $G$ is a group and $H$ is a subgroup, then the regular action of $G$ on itself is inside of the action of the wreath product $H\wr (G/\mathrm{Core}(H))$ on $H\times G/H$ via the identification of $G$ with $H\times G/H$  using a transversal $T$ for $G/H$ and that replacing $T$ by a different transversal changes the embedding of $G$ by an inner automorphism of the wreath product. 
I am aware that this result is implicit in Frobenius's theory of induced representations and the theory of monomial representations of groups (e.g. Chapter 4 this paper of Ore although $H$ is assumed finite index there) but these authors did not use the wreath product language to the best of my knowledge. 
Many people refer only to the special case where $N$ is normal as the Krasner-Kaloujnine embedding. I am now wondering which version they actually stated. The original paper does not seem easy to access by the obvious Google search.

REPLY [3 votes]: The original paper (part II of a three part series) is available here. Page 47 lists the theorem and  discusses in a footnote the relation with Ore's earlier work.
From what I understand, any series of subgroups is allowed in the embedding, they need not be normal.
A more limited version of their theorem is published in part III, available here, and this has caused some confusion.