Finite structurally uniform groups and commutative nilsemigroups

  • V. D. Derech

Abstract

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.
Published
25.08.2018
How to Cite
DerechV. D. “Finite Structurally Uniform Groups and Commutative Nilsemigroups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 8, Aug. 2018, pp. 1072-84, http://umj.imath.kiev.ua/index.php/umj/article/view/1618.
Section
Research articles