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What do Frobenius's,
Solomon's, and Iwasaki's theorems on divisibility in groups
have in common?
Elena K. Brusyanskaya, Anton A. Klyachko and Andrey V. Vasil’ev |
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Vol. 302 (2019), No. 2, 437–452
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Abstract |
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Our result contains as special cases the Frobenius theorem (1895) on the number of solutions to the equation in a group, the Solomon theorem (1969) on the number of solutions in a group to a system of equations having fewer equations than unknowns, and the Iwasaki theorem (1985) on roots of subgroups. There are other curious corollaries on groups and rings. |
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Keywords
equations in groups, Frobenius's theorem, Solomon's
theorem, Iwasaki's theorem
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Mathematical Subject Classification 2010
Primary: 20D60, 20F70
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Milestones
Received: 11 July 2018
Revised: 12 January 2019
Accepted: 20 January 2019
Published: 27 November 2019
|
Authors |
| Elena K. Brusyanskaya | |
| Faculty of Mechanics and
Mathematics Moscow State University Moscow Russia |
|
| Anton A. Klyachko | |
| Faculty of Mechanics and
Mathematics Moscow State University Moscow Russia |
|
| Andrey V. Vasil’ev | |
| Sobolev Institute of
Mathematics Novosibirsk Russia |
Novosibirsk State University Novosibirsk Russia |
