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Nilʹpotentni pidnapivgrupy napivgrup peretvorenʹ : diseracija na zdobuttja naukokovogo stupenja kandidata fiziko-matematičnih naukKudryavtseva, GannaThe dissertation "Nilpotent subsemigroups of transformation semigroups" is devoted to the study of nilpotent subsemigroups of the symmetric inverse semigroup ▫${\mathcal{IS}}(M)$▫ and the semigroup ... ▫${\mathcal P}Aut_q(V_n)$▫ of all partial automorphisms of a finite vector space. For the semigroups ▫${\mathcal{IS}}(M)$▫ and ▫${\mathcal P}Aut_q(V_n)$▫ we describe the structure of subsemigroups, which are maximal among nilpotent subsemigroups of a fixed nilpotency degree. We establish isomorphism criterion of maximal nilpotent subsemigroups of the semigroup ▫${\mathcal{IS}}(M)$▫ for the case, when ▫$M$▫ is a countable set. We introduce the notion of linear types of linear orders on the set of lines of a finite vector space, and in its terms we establish an isomorphism criterion for maximal nilpotent subsemigroups of the semigroup ▫${\mathcal P}Aut_q(V_n)$▫. We prove that the group of automorphisms of a maximal nilpotent subsemigroup of the semigroup ▫${\mathcal{IS}}(M)$▫ (where ▫$M$▫ is at most countable) is isomorphic to a semidirect product of direct sums of symmetric groups. For maximal nilpotent subsemigroups of ▫${\mathcal{IS}}(M)$▫, ▫$M$▫ being finite, we investigate the structure of their lattices of ideals and compute some combinatorial characteristics of these lattices. The methods and the results of the dissertation can be applied for the further study of nilpotent subsemigroups of different transformation semigroups.Type of material - dissertationPublication and manufacture - Kyïv : [G. M. Šafranova], 2000Language - ukrainianCOBISS.SI-ID - 15600217
Author
Kudryavtseva, Ganna
Other authors
Ganjuškin, Oleksandr Grygorovyč
Topics
matematika |
algebra |
nilpotentna polgrupa |
podpolgrupa |
simetrična inverzna polgrupa |
delni avtomorfizem |
končni vektorski prostor |
grupa avtomorfizmov polgrupe |
maksimalna nilpotentna podpolgrupa |
mreže idealov polgrupe |
mathamatics |
algebra |
nilpotent semigroup |
subsemigroup |
symmetric inverse semigroup |
partial automorphism |
finite vector space |
automorphism group of a semigroup |
maximal nilpotent subsemigroups |
lattices of ideals of a semigroup
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Kudryavtseva, Ganna | 30109 |
Ganjuškin, Oleksandr Grygorovyč | ![]() |
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