Isoclinic groups have same commuting fraction

Statement

For finite groups

Suppose $G_{1},G_{2}$ are finite groups that are isoclinic to each other. Then, the commuting fraction of $G_{1}$ equals the commuting fraction of $G_{2}$.

For arbitrary groups

Suppose $G_{1},G_{2}$ are isoclinic groups such that $G_{1}$ is a FZ-group. Then, $G_{2}$ is also a FZ-group and the commuting fractions of $G_{1}$ and $G_{2}$ are equal.

Related facts

• Isologic groups have same fixed-class tuple fraction