Finitary alternating group of countable degree

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VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

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