Commuting fraction of direct product is product of commuting fractions

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Statement

For two groups

Suppose G_1 and G_2 are finite groups, the commuting fraction of G_1 is p_1 and the commuting fraction of G_2 is p_2. Then, the commuting fraction of the external direct product G_1 \times G_2 is the product p_1p_2.

For multiple groups

The commuting fraction of an external direct product is the product of the commuting fractions of each of the direct factors.

In symbols, if G_1, G_2, \dots, G_n are finite groups and p_1,p_2,\dots,p_n are their commuting fractions, then the external direct product G_1 \times G_2 \times \dots \times G_n has commuting fraction equal to the product p_1p_2\dots p_n.