 While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group  } on the natural numbers . } We show that this new subgroup contains the bounded symmetric group on the natural numbers, and consequently is highly transitive.
<others>  While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group  } on the natural numbers . } We show that this new subgroup contains the bounded symmetric group on the natural numbers, and consequently is highly transitive.
 While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group } on the natural numbers . N} We show that this new subgroup contains the bounded symmetric group on the natural numbers, and consequently is highly transitive.