L. I. Galieva, I. G. Galyautdinov, “One class of equations solvable in radicals”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 2,Pages <nobr>22

This article is cited in 4 papers

One class of equations solvable in radicals

L. I. Galieva, I. G. Galyautdinov

Chair of Algebra, Tatar State University of Humanities and Education, Kazan, Russia

Abstract: We derive recurrent formulas for obtaining minimal polynomials for values of tangents and show that Galois groups of these polynomials are commutative. Thus we give examples of equations of arbitrarily high degrees solvable in radicals.

Keywords: Euler function, modulo residue system, irreducible polynomial, numeric field finite extension, extension degree, circular polynomial, Galois groups of polynomials and field extensions.

UDC: 511.61

Received: 30.06.2009