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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
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