Automorphism group of finitary symmetric group equals symmetric group | | Symmetric group (?) Finitary symmetric group (?) |

Classification of symmetric groups that are N-groups | | Symmetric group (3) N-group (3) |

Conjugacy class of transpositions is the unique smallest conjugacy class of involutions | | Transposition (?) Symmetric group (?) Conjugacy class (?) |

Cycle type determines conjugacy class | | Cycle type of a permutation (1) Conjugate elements (2) Symmetric group (3) Conjugacy class (3) |

Finitary alternating group is characteristic in symmetric group | | Alternating group (?) Characteristic subgroup (?) Symmetric group (?) |

Finitary alternating group is conjugacy-closed in symmetric group | | Alternating group (?) Conjugacy-closed subgroup (?) Symmetric group (?) Conjugacy-closed normal subgroup (?) |

Finitary alternating group is intermediately monolith in symmetric group | | Alternating group (?) Monolith (?) Symmetric group (?) |

Finitary symmetric group equals center of symmetric group modulo finitary alternating group | | Symmetric group (?) Finitary symmetric group (?) Alternating group (?) Center (?) |

Finitary symmetric group is automorphism-faithful in symmetric group | | Finitary symmetric group (?) Automorphism-faithful subgroup (?) Symmetric group (?) |

Finitary symmetric group is centralizer-free in symmetric group | | Finitary symmetric group (?) Centralizer-free subgroup (?) Symmetric group (?) |

Finitary symmetric group is characteristic in symmetric group | | Finitary symmetric group (?) Characteristic subgroup (?) Symmetric group (?) |

Finitary symmetric group is locally inner automorphism-balanced in symmetric group | | Finitary symmetric group (?) Locally inner automorphism-balanced subgroup (?) Symmetric group (?) |

Finitary symmetric group is normal in symmetric group | | Finitary symmetric group (?) Normal subgroup (?) Symmetric group (?) |

Finitary symmetric group is not fully invariant in symmetric group | | Finitary symmetric group (?) Fully invariant subgroup (?) Symmetric group (?) |

Isotropy of finite subset has finite double coset index in symmetric group | | Subgroup of finite double coset index (?) Symmetric group (?) |

Number of conjugacy classes of subgroups in symmetric group is logarithmically bounded by square of degree | | Symmetric group (?) Symmetric group on finite set (?) |

Subgroup rank of symmetric group is about half the degree | | Symmetric group (3) Subgroup rank of a group (2) |

Symmetric group on a finite set is 2-generated | 2 | Symmetric group (?) 2-generated group (?) Minimum size of generating set (?) |

Symmetric group on a finite set is a Coxeter group | | Symmetric group (?) Coxeter group (?) |

Symmetric group on finite or cofinite subset is conjugacy-closed | | Conjugacy-closed subgroup (?) Symmetric group (?) |

Symmetric group on finite or cofinite subset is subset-conjugacy-closed | | Subset-conjugacy-closed subgroup (?) Symmetric group (?) |

Symmetric group on finite set has Sylow subgroup of prime order | | Symmetric group (?) Symmetric group on finite set (?) Sylow subgroup (?) Group of prime order (?) |

Symmetric group on infinite coinfinite subset is not conjugacy-closed | | Conjugacy-closed subgroup (?) Symmetric group (?) |

Symmetric groups are almost simple | | Symmetric group (?) Almost simple group (?) |

Symmetric groups are ambivalent | | Symmetric group (?) Ambivalent group (?) |

Symmetric groups are normal-comparable | | Symmetric group (?) Group in which any two normal subgroups are comparable (?) |

Symmetric groups are rational | | Symmetric group (?) Rational group (?) |

Symmetric groups are rational-representation | | Symmetric group (?) Rational-representation group (?) |

Symmetric groups are strongly ambivalent | | Symmetric group (?) Strongly ambivalent group (?) Strongly real element (?) |

Symmetric groups on finite sets are complete | | Symmetric group (?) Symmetric group on finite set (?) Complete group (?) Group in which every automorphism is inner (?) |

Transposition-preserving automorphism of finitary symmetric group is induced by conjugation by a permutation | | Symmetric group (?) Finitary symmetric group (?) |

Transposition-preserving automorphism of symmetric group is inner | | Symmetric group (?) Transposition (?) |

Transpositions generate the finitary symmetric group | | Finitary symmetric group (2) Transposition (2) Symmetric group (?) Transposition (?) Finitary symmetric group (?) |

Transpositions of adjacent elements generate the symmetric group on a finite set | | Transposition (?) Symmetric group (?) |

Weakly normal subgroup of symmetric group must move more than half the elements | | Symmetric group (?) Weakly normal subgroup (?) Pronormal subgroup (?) Paranormal subgroup (?) Polynormal subgroup (?) |