# Prime power order implies nilpotent for Moufang loops

From Groupprops

ANALOGY: This is an analogue in Moufang loops of a fact encountered in group. The old fact is: prime power order implies nilpotent.

View other analogues of prime power order implies nilpotent|View other analogues from group to Moufang loop (OR, View as a tabulated list)

## Statement

Suppose is a Moufang loop of prime power order, i.e., a Moufang loop whose underlying set has order a prime power. Then, is a nilpotent Moufang loop (i.e., a finite nilpotent Moufang loop).

## Related facts

### Similar facts

- Prime power order implies nilpotent (in groups)