What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common?

DOI10.2140/pjm.2019.302.437OpenAlexW2810657755WikidataQ126671365 ScholiaQ126671365MaRDI QIDQ2305388

Anton A. Klyachko, Elena K. Brusyanskaya, Andrey V. Vasilev

Publication date: 10 March 2020

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.08870

zbMATH Keywords

equations in groupsFrobenius's theoremIwasaki's theoremSolomon's theorem

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Algebraic geometry over groups; equations over groups (20F70)

Related Items (2)

On the number of epi-, mono- and homomorphisms of groups ⋮ The dimension of solution sets to systems of equations in algebraic groups

Cites Work

• On the divisibility of \(\#\Hom(\Gamma,G)\) by \(|G|\).
• Strange divisibility in groups and rings
• \(|\Hom(A,G)|\). II.
• 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 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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