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Order statistics of a finite group

146 bytes added, 22:26, 24 June 2009
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The '''order statistics''' of a [[finite group]] is a function <math>\mathbb{N}_0 \to \mathbb{N}_0</math> which takes <math>n</math> and outputs the number of elements <math>x</math> whose order is <math>n</math>.
If <math>f</math> denotes the order statistics function, then the [[number:Dirichlet convolution|Dirichlet convolution ]] <math>F = f * U</math> gives, for each <math>n</math>, the number of elements <math>x</math> satisfying <math>x^n = e</math>. Two finite groups that have the same order statistics are termed [[order statistics-equivalent finite groups]].
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