Galois groups for one class of equations

Abstract

We find recurrent formulas for obtaining minimal polynomials p n(x) ∈ Z[x] of numbers of the form cos pi/n, where n ∈ N. We demonstrate that Galois groups of these polynomials are commutative. By the same token we give examples of equations of arbitrarily high degrees solvable in radicals. © 2011 World Scientific Publishing Company