We prove that a locally graded group whose proper subgroups are Engel (respectively, k-Engel) is either Engel (respectively, k-Engel) or finite. We also prove that a group of infinite rank whose proper subgroups of infinite rank are Engel (respectively, k-Engel) is itself Engel (respectively, k-Engel), provided that G belongs to the Cernikov class X, which is the closure of the class of periodic locally graded groups by the closure operations P, P, R and L.
展开▼
