Algebra

1903 Submissions

[1] viXra:1903.0099 [pdf] submitted on 2019-03-05 06:31:22

Finite Faithful G-Sets Are Asymptotically Free

Authors: Pierre-Yves Gaillard
Comments: 3 Pages.

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.
Category: Algebra