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 $A \in Sub(S)$, then by $h(A)$ wedenote the height of the subsemigroup $A$ in the lattice $Sub(S)$. A semigroup $S$ is called structurally uniform if, for any$A, B \in Sub(S)$ the condition $h(A) = h(B) implies that A \sim = B$. We present a classification of finite structurally uniformgroups and commutative nilsemigroups.