On the divisibility of \(\#\Hom(\Gamma,G)\) by \(|G|\).

DOI10.1016/j.jalgebra.2011.09.040zbMath1260.20066arXiv1105.6066OpenAlexW106931706MaRDI QIDQ420729

Fernando Rodriguez Villegas, Cameron McA. Gordon

Publication date: 23 May 2012

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

Full work available at URL: https://arxiv.org/abs/1105.6066

zbMATH Keywords

finitely generated groupsrepresentation spacesnumbers of subgroups of given index

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Subgroup theorems; subgroup growth (20E07) Automorphisms of infinite groups (20E36) Special aspects of infinite or finite groups (20F99)

Related Items (7)

On the number of epi-, mono- and homomorphisms of groups ⋮ The dimension of solution sets to systems of equations in algebraic groups ⋮ E-series of character varieties of non-orientable surfaces ⋮ Strange divisibility in groups and rings ⋮ The number of monodromy representations of abelian varieties of low \(p\)-rank ⋮ What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common? ⋮ How many tuples of group elements have a given property? With an appendix by Dmitrii V. Trushin

Cites Work

• Arithmetic harmonic analysis on character and quiver varieties
• The solution of equations in groups
• Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces
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