Finite faithful G-sets are asymptotically free
| Autor: | Gaillard, Pierre-Yves |
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| Rok vydání: | 2022 |
| Předmět: | |
| DOI: | 10.5281/zenodo.6573067 |
| Popis: | 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 leastE(n(i-1)/4)/k for i>1. |
| Databáze: | OpenAIRE |
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