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Sylow Theorems

In: Group Theory

Author

Listed:
  • Dinesh Khattar

    (University of Delhi, Department of Mathematics)

  • Neha Agrawal

    (University of Delhi, Department of Mathematics)

Abstract

The Sylow theorems are an ensemble of results in the theory of finite groups. The common thread linking this chapter's theorems is that they determine group structure based on group order. They are results that are absolutely central to group theory, and they also serve as a partial converse to Lagrange's Theorem: ‘partial’ because it guarantees the existence of a subgroup only if its order is prime. They are named in honour of P. Ludwig Sylow, who published these theorems in the year 1872.

Suggested Citation

  • Dinesh Khattar & Neha Agrawal, 2023. "Sylow Theorems," Springer Books, in: Group Theory, chapter 0, pages 303-325, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-21307-6_11
    DOI: 10.1007/978-3-031-21307-6_11
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