In
mathematics, Shafarevich's theorem states that any
finite
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb
Traditionally, a finite verb (from la, fīnītus, past partici ...
solvable group
In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group (mathematics), group that can be constructed from abelian groups using Group extension, extensions. Equivalently, a solvable group is a ...
is the
Galois group
In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship to the po ...
of some
finite extension
In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — ...
of the
rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ra ...
s. It was first proved by , though
Alexander Schmidt later pointed out a gap in the proof, which was fixed by .
References
*
*
Galois theory
Solvable groups
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