I am trying to learn about wreath products in the context of group theory. I was following Rotman's book on the subject but I find it very difficult to follow and he makes some mistakes (for instance here).
Is there a concise and relatively simple text on this topic? I'm looking for a text which actually provides some intuition if possible.
Hopefully this is still interesting to you after 3 years, but I think I can give a graphical approach to wreathproducts that may help to give an intuition. I'm not too sure if this is completely correct, so read with caution:
Let $M$, $N$ be Monoids and $X$ an set. Further let $M^X \rtimes N$ be the semidirect product. Then there is $M^X = \{f \mid f: X \to M\}$ with $f, g \in M^X$ and $m, m' \in M$. Last there is $n,n' \in N$.
We now give an graphical interpretation of the "first" part of the tupel:
$$(f, n)(g,n') = (f+ng,nn')$$ If we apply this to an $x$ we get $$(f(x)+n\cdot g(x), nn') = (m + g(x'), nn') = (m + m', nn') = (\overline{m}, nn')$$