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Ukrainian Mathematical Congress 7 International Institute of Mathematics of National Academy of Sciences of Ukraine Taras Shevchenko Kiev National University V. N. Karazin Kharkov National University UKRAINIAN MATHEMATICAL CONGRESS 7th INTERNATIONAL ALGEBRAIC CONFERENCE IN UKRAINE 18–23 August, 2009 ABSTRACTS OF TALKS Kharkov – 2009 УÄÊ 512(063) ÁÁÊ 22.14 я 431 С28 7-ма Мiжнародна алгебраїчна êонференцiя в Українi: тези доповiдей (18–23 сер- пня 2009 року, Харкiв)/Вiдп. ред. Ã. М. Жолткевич. K.: 2009. 168 c. 7th International Algebraic Conference in Ukraine: abstracts of talks (18–23 August, 2009, Kharkiv)/ Ed. G. N. Zholtkevich. Kiev: 2009. 168P. У збiрнику мiстяться матерiали Сьомої мiжнародної алгебраїчної êонференцiї в Українi, присвяченої 120-рiччю вiд дня народження професора Харкiвського унiверситету Антона Казимiровича Сушкевича. The collection contains the abstracts of talks of 7th International Algebraic Conference in Ukraine dedicated to the 120th anniversary of Professor of Kharkiv University Anton Kazimi- rovich Sushkevich. Ðедакцiйна êолегiя: Жолткевич Ã. М., Новiков Á. Â., Полякова Ë. Ю., Хрипченко М. С. Адреса ред. êолегiї: 61077, м. Харкiв, пл. Свободи, 4, Харкiвський нацiональний унiверситет iменi Â. Í. Ка- разiна, механiко-математичний факультет, êаб. 6-62а, тел. 707-55-27, e-mail:[email protected]. Матерiали подаються в авторськiй редакцiї. Вiдповiдальнiсть за достовiрнiсть iнформа- цiї, êоректнiсть математичних викладок несуть автори. Тези доповiдей опублiковано мовою оригiналу. Посилання на матерiали збiрника обов’язковi. Ðекомендовано до друку вченою радою механiко-математичного факультету. Протокол № 5 вiд 15.05.2009. c Харкiвський нацiональний унiверситет ° iменi Â. Í. Каразiна, 2009 Kharkov, August 18-23, 2009 3 Contents K. Aghigh. On invariants of irreducible polynomials over a Henselian valued field . 9 K. Ahmadidelir, H. Doostie, A. Sadeghieh. pth roots of elements in finite groups . 9 S. A. Aleschenko, V. I. Arnautov. Completion of pseudonormed rings and semi-isometric isomorphism . 10 V. Andriychuk. On the elementary obstruction in linear algebraic groups over pseudoglobal fields . 11 A. Antonenko, E. Berkovich. Groups generated by slowmoving automata transformations . 12 G. Aranda Pino, E. Pardo, M. Siles Molina. Prime spectrum and primitive Leavitt path algebras . 12 V. I. Arnautov. About metrizable, linear, group topologies of the Abelian groups, which coincide on some subgroup and on some factor group . 13 O. D. Artemovych. Radical rings with center of finite index . 14 I. V. Arzhantsev, A. P. Petravchuk. On saturated subfields of invariants of finite groups . 15 A. Atkarskaya. Isomorphisms of the groups GLn(R), n > 4 over associated graded rings . 15 T. Banakh, S. Dimitrova and O. Gutik. The Rees-Suschkewitsch Theorem for simple topological semigroups . 16 L. F. Barannyk. Twisted group algebras of semi-wild representation type . 18 Yu. Bazilevich. Similarity transformation of the pair of matrices to the best partitioned-triangular form . 19 L. Bedratyuk. The Hilbert series of the algebras of joint invariants and covariants of two binary forms . 19 L. Bedratyuk, I. Kachuryk. Characters of Lie algebra sl3 and (q; p)-numbers . 21 А. Я. Белецкий. Алгебраические основы è приложения преобразований Грея . 22 G. Belozerov, P. Varbanets. On the average value of Dirichlet's convolutions of the functions ¿(n) and r(n) in arithmetic progressions . 23 G. Belyavskaya, T. Popovich. Totally conjugate-orthogonal quasigroups . 24 G. Belyavskaya, A. Tabarov. Postulates of Sushkevich and linear quasigroups . 25 S. I. Bilavska. Analog of Cohen's theorem for distributive Bezout domains . 26 S. I. Bilavska, B. V. Zabavsky. The speciality of the structure of two-sided ideals of elementary divisor domain . 26 Yu. Bodnarchuk, P. Prokofiev. Nagata's type automorphisms as the exponents of three root locally nilpotent derivations . 26 E. Bonacci, M. De Paz. Binomial properties with significant consequences about Fermat's equation and on the cosine rule . 27 I. Bondarenko, N. Bondarenko. Conjugation of finite-state automorphisms of regular rooted trees . 28 V. M. Bondarenko, M. V. Styopochkina. Classification of NP -critical posets . 29 V. M. Bondarenko, O. M. Tertychna. Quadratic forms of semigroups generated by idempotents with partial null multiplication . 30 V. V. Bondarenko. On triangular similarity of nilpotent matrices . 30 А. А. Борисенко. Биномиальные системы счисления . 31 E. Bunina. Automorphisms of Chevalley groups over rings . 32 N. Burban, O. Horbachuk. Some properties of the class in the category of modules over T different rings . 32 A. Chentsov. Free Category Generated by a Partial Semigroup . 33 I. Chernenko.The extensions of proper locally finite subgroups with quasicentral sylow 2-subgroups by the quaternion group . 34 V. A. Chupordya, L. A. Kurdachenko, I. Ya. Subbotin. On groups whose subgroups are either subnormal or pronormal . 35 4 7th International Algebraic Conference in Ukraine D. V. Chuprakov. About distributive property of lattices of semirings of continuous functions . 36 E. P. Cojuhari. Derivation Mappings on non-commutative rings . 36 O. Yu. Dashkova. Modules over group rings of locally soluble groups with rank restrictions on some systems of subgroups . 37 V. Derech. On group of automorphisms of some finite inverse semigroup . 38 I. I. Deriyenko. On prolongations of quasigroups with middle translations . 39 S. D. Dimitrova-Burlayenko. On connection between quasi-uniform convergence by Arcela and Alexandrov . 39 A. Dmytryshyn, V. Sergeichuk. Miniversal deformations of pairs of skew-symmetric forms . 40 O. Domsha, B. Zabavsky. Reduction of matrices over Kazimirsky domain . 41 V. Doroshenko.Free subsemigroups in topological semigroups . 42 Zh. Dovghey. Central series in the unitriangle automorphism group of the ring of two polynomi- als variable over the field of zero characteristic . 43 Y. Drozd. Titling theory and representations of linear groups over piecewise hereditary algebras . 43 M. G. Drushlyak. Finite p-groups (p = 2) with non-Abelian norm of Abelian non-cyclic 6 subgroups . 44 W. A. Dudek. Neutral elements in n-ary hyperalgebras . 45 S. Dyachenko. On modular representations of Rees semigroups over cyclic group of order two 46 N. Dzhalyuk. Equivalence and factorization of partitioned matrices . 47 S. Favorov, Ye. Kolbasina. On a property of discrete sets in Rks . 48 S. D. Friedman, L. Zdomskyy. Measurable Cardinals and the Cofinality of the Symmetric Group . 49 I. V. Fryz. About linear cross isotopes of linear quasigroups . 49 N. Fugelo, O. Savastru. Gaussian integers with divisors in narrow sectors . 50 S. S. Gabriyelyan. Characterization of almost maximally almost-periodic groups . 51 A. Gatalevich. Right Bezout rings with waists . 51 V. Gavrylkiv. The structure of minimal left ideals of the Superextensions of Abelian groups . 52 T. G. Gerasimova. Matrices that are self-congruent only via matrices of determinant one . 54 Sh. Ghalandarzadeh, P. Malakooti Rad. Torsion Graph Over Multiplication Modules . 55 Sh. Ghalandarzadeh, S. Shirinkam. Weakly Prime submodule . 56 R. Golamie. Fibonacci length and special automorphisms of (l; m n; k)-group . 56 j K. Golubev. Cayley graphs, dessins d'enfants and modular curves . 57 I. S. Grunsky, E. A. Pryanichnikova. On an algebra of languages representable by vertex-labeled graphs . 58 I. S. Grunsky, S. V. Sapunov. On minimal identifiers of the vertices of the vertex-labeled graphs . 59 S. V. Gudzenko. Relation on finitary factorpowers of SN . 60 J O. Gutik, J. Lawson and D. Repovˇs. Semigroup Closures of Finite Rank Symmetric Inverse Semigroups . 61 O. L. Horbachuk, M. Ya. Komarnytskyi, Yu. P. Maturin. Differential preradicals and differential preradical filters . 62 A. Husainov. Global dimension of polynomial rings in partially commuting variables . 63 O. Iena, A. Regeta. On centralizers of rational functions in the Lie algebra of derivations of k[x; y] . 63 Yu. Ishchuk, N. Zasjadkovych. On Algorithms Inverting the Burau Representation . 64 A. Karimi Feizabadi. Pointfree Representation of real lattice ordered linear map . 65 A. I. Kashu. On classes of modules and preradicals defined by functor HomR(U; -) . 66 N. Kaydan. Quivers of finite rings . 66 T. Kemoklidze. The Lattice of Fully Invariant Subgroups of Reduced Cotorsion Group . 67 Kharkov, August 18-23, 2009 5 Yu. Khomenko. Orientations of the Petersen graph . 68 N. Khripchenko. The isomorphism problem for finitary incidence rings . 69 M. A. Khybyna, V. V. Kyrychenko. On Right Serial Quivers . 70 V. V. Kirichenko, N. A. Bronickaya. Global dimension of semiperfect semidistributive prime rings . 71 A. Kizimenko. On the bands of semigroups . 71 E. N. Klimenko. Classification of linear operators on a 5-dimensional unitary space . 72 E. Kochubinska. Completely isolated subsemigroups of wreath product of inverse symmetric semigroups . 72 M. Komarnytskyi, M. Maloyid. Multiplication modules, in which every prime submodule is contained in unique maximal submodule . 73 M. Komarnitskyi, H. Zelisko. On commutative semigroups and splitting preradicals over them 74 A. Kostin. On 0-cohomology of completely 0-simple semigroups . 74 O. Kotova, M. Pratsiovytyi. On fractal properties of some Cantor-type sets related to Q-representation of real numbers . 75 F. Kovalchik, P. Varbanets. On generalization of the theorem of Ramachandra . 76 V. Kovaleva, A. Skiba. Characterizations of finite soluble and supersoluble groups . 77 V. Kovdrysh. The width of verbal subgroups of unitriangular matrices groups over ring of Z=mZ . 78 I. B. Kozhukhov. Posets which are acts
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