Semidirect Products

caspinelli Uncategorized June 6, 2018 1 Minute

The Direct Product, Semidirect Product, and General Product (which I don’t understand and will not cover) all solve the problem of understanding the structure of a group $G = HK$ where $H,K \leq G$ and $H \cap K = \{1\}$ . When $H,K \trianglelefteq G$ , then $G \cong H \times K$ .