Ivan Shishkin, Rye (1878)

Problems/General algebra

Les pp-Sylow de Sp\mathfrak S_{p}

by Étienne86·
42
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Soit pp un nombre premier. Trouver le nombre de pp-Sylow du groupe symétrique Sp\mathfrak S_{p}.
En déduire que (p−1)!(p-1)! est congru à −1-1 modulo pp.

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References

  1. Vidéo de Philippe Caldero
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