Finite structurally uniform groups and commutative nilsemigroups - Derech, V. D. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
Let S be a finite semigroup. By Sub(S) we denote the lattice of all its subsemigroups. If A Sub(S), then by h(A) we denote the height of the subsemigroup A in the lattice Sub(S). A semigroup S is called structurally uniform if, for any A, B Sub(S) the condition h(A) = h(B) implies that A = B. We present a classification of finite structurally uniform groups and commutative nilsemigroups.