Finitary symmetric group is characteristic in symmetric group

Statement
The fact about::finitary symmetric group on an infinite set is a fact about::characteristic subgroup of the fact about::symmetric group on that set.

Facts used

 * 1) uses::Finitary alternating group is monolith in symmetric group
 * 2) uses::Monolith is characteristic
 * 3) uses::Finitary symmetric group equals center of symmetric group modulo finitary alternating group
 * 4) uses::Characteristicity is quotient-transitive

Proof
The proof follows directly by combining facts (1)-(4).