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arXiv · 1806.08870

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

Elena K. Brusyanskaya·Anton A. Klyachko·Andrey V. Vasil'ev
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Abstract

Our result contains as special cases the Frobenius theorem (1895) on the number of solutions to the equation $x^n=1$ 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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Elena K. Brusyanskaya, Anton A. Klyachko, Andrey V. Vasil'ev. 2018-06-22. What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common?. https://doi.org/10.2140/pjm.2019.302.437

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