# Commuting fraction of direct product is product of commuting fractions

From Groupprops

## Statement

### For two groups

Suppose and are finite groups, the commuting fraction of is and the commuting fraction of is . Then, the commuting fraction of the external direct product is the product .

### 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 are finite groups and are their commuting fractions, then the external direct product has commuting fraction equal to the product .