We recently went through the wreath product in my group theory class, but the definition still seems a bit unmotivated to me. The two reasons I can see for it are 1) it allows us to construct new groups, and 2) we can use it to reconstruct imprimitive group actions. Are there any applications of […]

The Details: Let’s have a recap of some definitions (taken from “Nine Chapters in the Semigroup Art” (pdf), by A. J. Cain). Definition 1: Let $P$ be a semigroup. The left action of $P$ on a set $X$ is an operation $\cdot:P\times X\to X$ such that $(pq)\cdot x=p\cdot (q\cdot x)$ for all $x\in X$, $p, […]

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