#### Vol. 302, No. 2, 2019

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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

Vol. 302 (2019), No. 2, 437–452
##### 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.

##### Keywords
equations in groups, Frobenius's theorem, Solomon's theorem, Iwasaki's theorem
##### Mathematical Subject Classification 2010
Primary: 20D60, 20F70