# Finitary alternating group of countable degree

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## 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 |