|
In mathematics, Burnside's theorem in group theory states that if ''G'' is a finite group of order : where ''p'' and ''q'' are prime numbers, and ''a'' and ''b'' are non-negative integers, then ''G'' is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct primes. ==History== The theorem was proved by using the representation theory of finite groups. Several special cases of it had previously been proved by Burnside, Jordan, and Frobenius. John Thompson pointed out that a proof avoiding the use of representation theory could be extracted from his work on the N-group theorem, and this was done explicitly by for groups of odd order, and by for groups of even order. simplified the proofs. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Burnside theorem」の詳細全文を読む スポンサード リンク
|