Group closures of partial transformations
Tóm tắt
Let \(X\) be an infinite set, \(f\) a partial one-to-one transformation of \(X\), and \(H\) a normal subgroup of G
X
, the group of all permutations of \(X\). We investigate when \(H\) is equal to \(G_{}\). That is, we are interested when \(H\) is the full group of normalizers of the semigroup of transformations on \(X\) generated by conjugates of \(f\) by elements of \(H\).