Document Type
Article
Publication Date
2001
Publication Title
Cambridge University Press
Abstract
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.
Recommended Citation
Levi, Inessa, "Group closures of one-to-one transformations" (2001). Faculty Bibliography. 533.
https://csuepress.columbusstate.edu/bibliography_faculty/533
