i have a doubt about the Wreath Product Notation, for example on Wikipedia, or most internet pages (also some questions here on Mathstackexchange) i find :
The wreath product $A ≀ B$ of A by B is the semidirect product K ⋊ H, where K is a direct product of $|B|$ copies of A.
But then i find in some papers something like:
The wreath product A ≀ B is the semidirect product $B^A ⋊ A$, where A acts on $B^A$ by shifts
Which says the exact opposite... So i´m a Little confusing about the notation, which one should i use? or there is something that i´m missing? When i see $A ≀ B$ in a random paper i have to check wether it`s one definition or the other one..