On the Dirichlet polynomial of finite groups of Lie type. (Q833476)
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scientific article; zbMATH DE number 5595156
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Dirichlet polynomial of finite groups of Lie type. |
scientific article; zbMATH DE number 5595156 |
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On the Dirichlet polynomial of finite groups of Lie type. (English)
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13 August 2009
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Summary: For a given finite group \(G\) there exists a uniquely determined Dirichlet polynomial \(P_G(s)\) with the property that for \(t\in {\mathbb N}\) the number \(P_G(t)\) coincides with the probability of generating \(G\) by \(t\) randomly chosen elements. We discuss whether the isomorphism type of a simple group \(G\) can be determined by the knowledge of \(P_G(s)\).
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finite simple groups
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probabilistic zeta functions
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irreducible Dirichlet polynomials
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finite groups of Lie type
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