Examples
Many familiar p-groups are regular:
- Every abelian p-group is regular.
- Every p-group of nilpotency class strictly less than p is regular.
- Every p-group of order at most pp is regular.
- Every finite group of exponent p is regular.
However, many familiar p-groups are not regular:
- Every nonabelian 2-group is irregular.
- The Sylow p-subgroup of the symmetric group on p2 points is irregular and of order pp+1.
Read more about this topic: Regular P-group
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