## Finite Faithful G-Sets Are Asymptotically Free

**Authors:** Pierre-Yves Gaillard

Let G be a finite nontrivial group, let X be a finite faithful G-set, let P^i(X) be the i-th power set of X, let n(i) be the number of points of P^i(X), let m(i) be the number of points of P^i(X) with non-trivial stabilizer, let k be the number of prime order subgroups of G, and set E(j):=2^j for any integer j. We prove that n(i)/m(i) is at least E(n(i-1)/4)/k for i>1.

**Comments:** 3 Pages.

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### Submission history

[v1] 2019-03-05 06:31:22

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