Power statistics of a finite group

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Definition

The power statistics of a finite group G of order n can be viewed in the following ways:

  1. The non-cumulative power statistics is a function from the set of divisors of n to the nonnegative integers, which sends d to the number of elements g \in G for which there exists h \in G satisfying h^d = g but such that there is no larger divisor d' of n for which there exists k \in G with k^{d'} = g.
  2. The cumulative power statistics is a function from the set of divisors of n to the nonnegative integers, which sends d to the number of elements g \in G for which there exists h \in G satisfying h^d = g.

Related notions

Similar statistics

Related equivalence relations