الخميس، 6 يناير، 2011

Évariste Galois and group theory


Évariste Galois was French mathematician born on October 25, 1811 in Bourg-la-Reine.his talent was appeared in his teenage as he he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals. He was the first to use the word "group" 

Galois great efforts in mathematics is Galois theory.While Abel was the first to prove that some polynomial equations had no algebraic solutions, Galois established the necessary and sufficient condition for algebraic solutions to exist. He realized that the algebraic solution to a polynomial equation is related to the structure of a group of permutations associated with the roots of the polynomial, the Galois group of the polynomial. He found that an equation could be solvable in radicals if one can find a series of subgroups of its Galois group, each one normal its successor with abelian quotient, or its Galois group is solvable. This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations which Galois originally applied it to.


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