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  • ...tract algebra]]. In particular, heavy use is made of [[ring theory]] and [[Galois theory]]. Algebraic methods are particularly well-suited to studying proper ...ct of studying elliptic curves is the fact that there is a natural abelian group structure on its points. This means that given 2 points on the curve, they
    5 KB (849 words) - 15:14, 18 May 2021
  • ...mportant tool for the study of [[field]]s. The primary objects of study in Galois theory are [[automorphism]]s of fields. ...s <math>f</math> and <math>g</math> form a [[group]], called the '''Galois group''' of <math>K</math> over <math>\mathbb{Q}</math>.
    2 KB (385 words) - 13:09, 5 May 2008
  • ...ve]] [[function]] from a [[set]] of size <math>n</math> to itself, and the group operation is [[composition]] of functions. ...or example, an important theorem in [[Galois theory]] is that the [[Galois group]] of the general polynomial equation of degree <math>n</math> is <math>S_{n
    10 KB (1,668 words) - 14:33, 25 May 2008
  • ...group''' is a type of [[group]] of particular interest, particularly in [[Galois theory]]. ...ian]] if and only if its solvability class is at most one; it is [[trivial group |trivial]] if and only if its solvability class is zero.
    4 KB (711 words) - 16:04, 5 June 2008
  • ...hbb Q(\zeta_n):\mathbb Q]=2^m</math>. Thus <math>G</math> is a [[p-group|2-group]], and hence there must exist a chain of subgroups ...:G_i]=2</math> for all <math>i</math>. Now by the [[fundamental theorem of Galois theory]], if <math>K_i</math> is the fixed field of <math>G_i</math> then
    5 KB (926 words) - 17:47, 4 March 2022
  • ...for more exploration in other topics, including Set Theory, Group Theory, Galois Theory, and more.
    3 KB (474 words) - 19:48, 28 May 2013
  • ...ct, the collection of the <math>n</math>th roots of unity forms a cyclic [[group]] under multiplication, which we will call <math>\mathbb{U}</math>. ...gebraic number theory]] in particular, and also has some nice results in [[Galois theory]].
    8 KB (1,438 words) - 13:50, 23 June 2022
  • * [[Galois theory]] * [[Group theory]]
    434 bytes (46 words) - 15:11, 18 May 2021