Product of cartesian product set:$\times_c$:
\\
$(g_1,g_2,…g_t)\times_c(g'_1,g'_2,…g'_t)$
\\$=(g_1\circ  g'_1,g_2 \diamond g'_2,…,g_t\bullet g'_t)$

Product of cartesian product set

Product of $G_1,G_2,…,G_t$:
\\$(G_1\times G_2\times …\times G_t, \times_c )$

Product

Cartesian product factor of $(G_1×G_2×…×G_t, \times_c )$:\\$(G_1,\circ),(G_2,\diamond),…,(G_t,\bullet)$

Cartesian groups $(G_1,\circ),(G_2,\diamond),…,(G_t,\bullet)$
\\
are subgroup of $(G_1\times G_2\times …\times G_t, \times_c )$

$G_1\times G_2$ element in $G_1$a and $G_2$ are commutative

$\mathbb{Z}/mn\mathbb{Z}\simeq \mathbb{Z}/m\mathbb{Z}\times \mathbb{Z}/n\mathbb{Z}$