Cambridge University Press
A semigroup of transfonnations of an infinite set X is called ^'x-normal if S is invariant under conjugations by permutations of X. In this paper we describe injective endomorphisms of & x -normal semigroups of total one-to-one transformations / such that the range of / has a finite non-empty complement in X.
Levi, Inessa, "Injective endomorphisms of 풢x-normal semigroups: Finite defects." (1994). Faculty Bibliography. 604.