03-02. More on Cosets and lagrange’s theorem

Definition. product

• $G$
  • group
• $H, K \subseteq G$,
  • subgroups

\[\begin{eqnarray} HK & := & \{ hk \mid h \in H, \ k \in K \} \nonumber \\ & = & \bigcup_{h \in H} hK \nonumber \end{eqnarray} .\]

■

Proposition 14.

proof.

$\Box$