Finite structurally uniform groups and commutative nilsemigroups

  • V. D. Derech


Let $S$ be a finite semigroup. By $\mathrm{S}\mathrm{u}\mathrm{b}(S)$ we denote the lattice of all its subsemigroups. If $A \in \mathrm{S}\mathrm{u}\mathrm{b}(S)$, then by $h(A)$ we denote the height of the subsemigroup $A$ in the lattice $\mathrm{S}\mathrm{u}\mathrm{b}(S)$. A semigroup $S$ is called structurally uniform if, for any $A, B \in \mathrm{S}\mathrm{u}\mathrm{b}(S)$ the condition $h(A) = h(B) implies that A \sim = B$. We present a classification of finite structurally uniform groups and commutative nilsemigroups.
How to Cite
Derech, V. D. “Finite Structurally Uniform Groups and Commutative Nilsemigroups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 8, Aug. 2018, pp. 1072-84,
Research articles