Semigroups with few endomorphisms
Vlastimil Dlab, B. Neumann · Journal of the Australian Mathematical Society · 1969
Large finite groups have large automorphism groups [4]; infinite groups may, like the infinite cyclic group, have finite automorphism groups, but their endomorphism semigroups are infinite (see Baer [1, p. 530] or [2, p. 68]). We show in this paper that the corresponding propositions for semigroups are false.