On the Dirichlet polynomial of finite groups of Lie type
On the Dirichlet polynomial of finite groups of Lie type
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 \(P_G(s)\).
- University of Padua Italy
probabilistic zeta function; Dirichlet polynomials, finite simple groups, probabilistic zeta functions, Probabilistic methods in group theory, irreducible Dirichlet polynomials, finite groups of Lie type, Simple groups: alternating groups and groups of Lie type, Other Dirichlet series and zeta functions, Series and lattices of subgroups
probabilistic zeta function; Dirichlet polynomials, finite simple groups, probabilistic zeta functions, Probabilistic methods in group theory, irreducible Dirichlet polynomials, finite groups of Lie type, Simple groups: alternating groups and groups of Lie type, Other Dirichlet series and zeta functions, Series and lattices of subgroups
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