Why quintic polynomial equations are not solvable in radicals

Křížek, Michal, and Somer, Lawrence. "Why quintic polynomial equations are not solvable in radicals." Application of Mathematics 2015. Prague: Institute of Mathematics CAS, 2015. 125-131. <http://eudml.org/doc/287786>.

@inProceedings{Křížek2015,
abstract = {We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed by radicals, i.e., by the operations $+,\,-,\,\cdot ,\,:\,$, and $\@root n \of \{\cdot \}$. Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals.},
author = {Křížek, Michal, Somer, Lawrence},
booktitle = {Application of Mathematics 2015},
keywords = {Galois theory; finite group; permutation; radical},
location = {Prague},
pages = {125-131},
publisher = {Institute of Mathematics CAS},
title = {Why quintic polynomial equations are not solvable in radicals},
url = {http://eudml.org/doc/287786},
year = {2015},
}

TY - CLSWK
AU - Křížek, Michal
AU - Somer, Lawrence
TI - Why quintic polynomial equations are not solvable in radicals
T2 - Application of Mathematics 2015
PY - 2015
CY - Prague
PB - Institute of Mathematics CAS
SP - 125
EP - 131
AB - We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed by radicals, i.e., by the operations $+,\,-,\,\cdot ,\,:\,$, and $\@root n \of {\cdot }$. Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals.
KW - Galois theory; finite group; permutation; radical
UR - http://eudml.org/doc/287786
ER -