Growth series of finite extensions of \(Z^ n \)are rational

DOI10.1007/BF01394026zbMath0498.20022MaRDI QIDQ1171135

Max Benson

Publication date: 1983

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143046

zbMATH Keywords

growth seriesweightsubgroup of finite index

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Extensions, wreath products, and other compositions of groups (20E22)

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Cites Work

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• Linear Diophantine equations and local cohomology
• The combinatorial structure of cocompact discrete hyperbolic groups
• Mathematical crystal growth. I. II
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• The orders of the finite Chevalley groups
• A note on curvature and fundamental group
• Growth of finitely generated solvable groups
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• Linear homogeneous Diophantine equations and magic labelings of graphs
• The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups