2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62241We investigate some situation in which automorphisms of a group G are uniquely determined by their restrictions to a proper subgroup H. Much of the paper is devoted to studying under which additional hypotheses this property forces G to be nilpotent if H is. As an application we prove that certain countably infinite locally nilpotent groups have uncountably many (outer) automorphisms.14 pages - no figures - to appear on Forum Mathematicum --- plain TeX requires eplain + additional macros filesGroup Theory20F28, 20F19text