# Finitary alternating group of countable degree

From Groupprops

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## Definition

The **finitary alternating group of countable degree** is the finitary alternating group over a set of countable size. In other words, it is the subgroup of the symmetric group of countable degree comprising the even permutations.

## Group properties

Property | Satisfied | Explanation |
---|---|---|

abelian group | No | |

nilpotent group | No | |

solvable group | No | |

simple group | Yes | The group is an infinite simple non-abelian group, because finitary alternating groups are simple |

locally finite group | Yes | |

finitely generated group | No |