The Sylow Theorems
We would like to know as much as possible about the subgroups of an arbitrary finite group. As might be expected very little can be said at this level of generality. However, around 1872 the Norwegian mathematician Sylow discovered some remarkable theorems about certain subgroups of any finite group. (See ‘Théorèmes sur les groupes de substitutions’— Mathematische Annalen. V (1872), pp. 584 et seq. - Sylow.)
KeywordsNormal Subgroup Finite Group Double Coset Distinct Solution Left Coset
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