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    P-group

    Definition

    When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of elements in G is a power of p. In fact, every finite group has subgroups which are p-groups by the Sylow theorems, in which case they are called Sylow p-subgroups.

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