Inessa Levi

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Cambridge University Press


For a semigroup 5 of transformations of an infinite set X let Gs be the group of all the permutations of X that preserve 5 under conjugation. Fix a permutation group H on X and a transformation / of X, and let (/ : H) = ({hfh~l : h 6 H}) be the //-closure of /. We find necessary and sufficient conditions on a one-to-one transformation / and a normal subgroup H of the symmetric group on X to satisfy G(f-.H) = H. We also show that if S is a semigroup of one-to-one transformations of X and Gs contains the alternating group on X then Aut(S) - Inn(S) = GS.

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Mathematics Commons