Periodicity of free subgroup numbers modulo prime powers

DOI10.1016/j.jalgebra.2015.12.026zbMath1331.05020arXiv1404.1258OpenAlexW2962686537MaRDI QIDQ5964507

Christian Krattenthaler, Thomas W. Müller

Publication date: 29 February 2016

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.1258

zbMATH Keywords

modular groupperiodic sequencesfree subgroup numbersvirtually free groups

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Subgroup theorems; subgroup growth (20E07) Algebraic combinatorics (05E99) Congruences; primitive roots; residue systems (11A07) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (2)

Free subgroup numbers modulo prime powers: the non-periodic case ⋮ Normalising graphs of groups

Cites Work

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• A Riccati differential equation and free subgroup numbers for lifts of \(\mathrm{PSL}_2(\mathbb Z)\) modulo prime powers
• A method for determining the mod-\(2^k\) behaviour of recursive sequences, with applications to subgroup counting
• A group-theoretical generalization of Pascal's triangle
• Decomposable functors and the exponential principle
• Poincaré complexes. I
• On torsion-free groups with infinitely many ends
• Modular arithmetic of free subgroups
• Combinatorial Aspects of Finitely Generated Virtually Free Groups

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