### Abstract

These theories extend the existing proof of the first Sylow theorem (written by Florian Kammueller and L. C. Paulson) by what are often called the second, third and fourth Sylow theorems. These theorems state propositions about the number of Sylow p-subgroups of a group and the fact that they are conjugate to each other. The proofs make use of an implementation of group actions and their properties.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Secondary_Sylow

- GroupAction
- SubgroupConjugation
- SndSylow

### Used by

- The Jordan-Hölder Theorem

## Cite

×

Secondary_Sylow-AFP

    @article{Secondary_Sylow-AFP,
      author  = {Jakob von Raumer},
      title   = {Secondary Sylow Theorems},
      journal = {Archive of Formal Proofs},
      month   = {January},
      year    = {2014},
      note    = {\url{https://isa-afp.org/entries/Secondary_Sylow.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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