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It is proved that the maximum condition for subloops in a commutative Moufangloop $Q$ is equivalent with the conditions of finite generating of differentsubloops of the loop $Q$ and different subgroups of the multiplication group ofthe loop $Q$. An analogue equivalence is set for the commutative Moufang$ZA$-loops.

The commutative Moufang loops with maximum conditions for subloops