On the number of epi-, mono- and homomorphisms of groups

DOI10.1070/IM9139MaRDI QIDQ5078308

Elena K. Brusyanskaya, Anton A. Klyachko

Publication date: 23 May 2022

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.03123

zbMATH Keywords

equations in groupsFrobenius' theoremnumber of homomorphismsSolomon's theorem

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Algebraic geometry over groups; equations over groups (20F70)

Cites Work

• On the divisibility of \(\#\Hom(\Gamma,G)\) by \(|G|\).
• Strange divisibility in groups and rings
• A generalization of Sylow's third theorem
• A note on the \(n\)th roots ratio of a subgroup of a finite group
• \(|\Hom(A,G)|\).
• The dimension of solution sets to systems of equations in algebraic groups
• What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common?
• The solution of equations in groups
• On a theorem of P. Hall
• How many tuples of group elements have a given property? With an appendix by Dmitrii V. Trushin
• CHARACTERS AND SOLUTIONS TO EQUATIONS IN FINITE GROUPS
• On P. Hall's Generalisation of a Theorem of Frobenius
• On the theory of equations in finite groups
• On A Theorem of Frobenius
• Systems of equations and generalized characters in groups
• \(|\Hom(A,G)|\). IV

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