http://dspace.nbuv.gov.ua:80/handle/123456789/188468 2026-04-22T13:00:30Z http://dspace.nbuv.gov.ua:80/handle/123456789/188572 Endomorphisms of Clifford semigroups with injective structure homomorphisms Worawiset, S.; Koppitz, J. In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα ∪ Gβ (α > β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188571 On a product of two formational tcc-subgroups Trofimuk, A. A subgroup A of a group G is called tcc-subgroup in G, if there is a subgroup T of G such that G = AT and for any X ≤ A and Y ≤ T there exists an element u ∈ hX, Y i such that XYᵘ ≤ G. The notation H ≤ G means that H is a subgroup of a group G. In this paper we consider a group G = AB such that A and B are tcc-subgroups in G. We prove that G belongs to F, when A and B belong to F and F is a saturated formation of soluble groups such that U ⊆ F. Here U is the formation of all supersoluble groups. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188570 Geometrical equivalence and action type geometrical equivalence of group representations Simoes da Silva, J.; Tsurkov, A. In this paper we construct an example of two representations (V₁,G₁) and (V₂,G₂) which are action type geometrically equivalent and groups G₁ and G₂ are geometrically equivalent, but the representations (V₁,G₁) and (V₂,G₂) are not geometrically equivalent. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188569 Energy of Smith graphs Sharma, P.; Naresh, R.; Sharma, U. In this manuscript, we have evaluated the energies of Smith graphs. In the course of the investigation, we found that only one Smith graph is hypo-energetic. Moreover, we have also established the energy bounds for Smith graphs. 2020-01-01T00:00:00Z