ON RELATIVE RANKS OF FULL TRANSFORMATION SEMIGROUPS

For a semigroup S and a set A subset of or equal to S the relative ran k of S module A is the minimal cardinality of a set B such that A bool ean OR B generates S. We show that the relative rank of an infinite fu ll transformation semigroup module the symmetric group, and also modul e the set of all idempotent mappings, is equal to 2. We also character ise all pairs of mappings which, together with the symmetric group or the set of all idempotents, generate the full transformation semigroup .