The X-Dirichlet polynomial of a finite group

DOI10.1515/jgth.2005.8.2.171zbMath1090.20038OpenAlexW2060715571MaRDI QIDQ4669776

Andrea Lucchini

Publication date: 15 April 2005

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgth.2005.8.2.171

zbMATH Keywords

finite groupssubgroup latticesnumbers of generatorsfactorizationschief factorsrandom elementsDirichlet polynomialsprobabilistic zeta functions

Mathematics Subject Classification ID

Series and lattices of subgroups (20D30) Generators, relations, and presentations of groups (20F05) Probabilistic methods in group theory (20P05)

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The expected number of random elements to generate a finite group ⋮ The limiting distribution of the product replacement algorithm for finitely generated prosoluble groups ⋮ Bias of group generators in finite and profinite groups: known results and open problems ⋮ Subgroups of solvable groups with non-zero Möbius function ⋮ The generating graph of finite soluble groups. ⋮ The diameter of the generating graph of a finite soluble group ⋮ On boundedly generated subgroups of profinite groups. ⋮ ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH ⋮ The minimum generating set problem ⋮ Recognizing the prime divisors of the index of a proper subgroup. ⋮ Bias of group generators in the solvable case. ⋮ Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function. ⋮ On the subgroups with non-trivial Möbius number ⋮ Profinite groups in which the probabilistic zeta function has no negative coefficients

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