# Department of Algebra and Differential Equations

#### Historical Reference

The Department of Algebra is a successor of the General Mathematics Department, founded September, 1, 1950. The heads of the department were Professor M. O. Zarytskyi, Associate Professor V. I. Sevbo, Professor S. D. Berman and the then Associate Professor P. M. Gudivok. In April, 1969, The Department of General Mathematics was renamed into The Department of Algebra which was headed by Professor Hudyvok till 2012. In the seventies the department was for some time headed by Associate Professor H. R. Rossa. Professors N. N. Aizenberg, A. A. Bovdi, Associate Professors S. S. Poliak, E. S. Drobotenko, V. S. Drobotenko, Z. P. Zhylinska, V. P. Rudko, P. H. Senior Lecturer I. Y. Shulla were working at the department during many years. M. D. Babych, L. F. Barannyk and F. H. Vashchuk worked at the department for some time, now they are Doctors of Sciences. Besides, PhDs O. I. Tsytkin, T. M. Sapuzhak, M. A. Dokuchaiev, A. A. Sakach and V. A. Bovdi worked as research workers at the department. The present staff of the department numbers 8 teachers: Associate Professor I. V. Shapochka (head of the department), Associate Professors Y. Y. Pohoriliak, O. A. Kyryliuk, V. F. Barannyk, O. A. Tylyshchak, N. V. Yurchenko and the lecturers M. P. Zhelizniak, A. O. Kyryliuk.

All the teachers and lecturers of the Department of Algebra are the graduating students of the Faculty of Mathematics, Uzhhorod University; all the Associate Professors have the degree of Candidate of Physics and Mathematics , speciality 01.01.06., “*algebra and the theory of numbers*” (scientific supervisor - Professor P. M. Hudyvok). L. I. Kozhara works as a senior laboratory assistant of the Department of Algebra.

The Department of Algebra provides lecturing on 14 general courses of study and 9 elective courses.

#### Scientific achievements

Scientific achievements of the Department of Algebra started in Uzhhorod State University in 1952 at the Department of General Mathematics headed by Associate Professor S. D. Berman. S. D. Berman achieved fundamental results on the representation of finite groups over the arbitrary field. He generalized at the arbitrary field the results of Brauer and Frobenius on inductive characters and the number of representations of finite groups over the algebraic closed field. Intensive investigations in the theory of representations of finite groups over commutative rings have been carried on since 1961. S. D. Berman and P. M. Hudyvok solved the problem on the number of simple representations of finite groups over the rings of integers and p-adic integers. The generalization of the results on some commutative local rings was done by P. M. Hudyvok, V. Y Pohoriliak and V. M. Oros. The relation between whole-number P-adic representations of a finite group and its subgroup was studied (Berman, Hudyvok, Rudko, Sapuzhak). V. S. Drobotenko , E. S. Drobotenko, Z. P. Zhylinska and Ye. Ya. Pohoriliak described all the simple representations of the groups of simple order *p *over the ring of the class of remainders under *module p**ᶺ**n . *This result was used by V. S. Drobotenko for the description of a finite *p-group* class. P. H. Hres proved one of hypotheses by Alperin. S. S. Poliak and V. P. Rudko have found a series of algorithms for describing classes of joined elements of the group of unitary matrices over the finite field.

E. S. Drobotenko described complex representations of groups GL (n, q) (n ˂= 4), Sudzuki G (q) group and the simple group of Yanko. L. F. Barannyk, V. F. Barannyk and P. M. Hudyvok investigated the project representation of finite groups over commutative local rings. They solved the problem of elementary project matrix representations of a finite group over the ring of P-adic integers. Lately, the theory of finite groups representations has been used by the co-workers of the Department of Algebra according to the investigation of definite classes of groups. P. M. Hudyvok, V. p. Rudko, O. A. Kyryliuk, P. H. Hres, O. I. Tsytkin described a series of important classes of finite subgroups of the full linear group over the ring of integers. V. A. Bovdi, P. M. Hudyvok, V. P. Rudko described a series of classes of crystallographic groups. Descriptions of several classes of p-groups by Chernikov have been given.

Seven alumni of the department became Doctors of Sciences and Professors (P. M. Hudyvok, AA Bovdi, L. F. Barannyk, A. F. Barannyk, A.I. Klimyk, K. Buzashi, F. H. Vashchuk). More than 40 graduates of the department became Candidates of Sciences (Ph.D.)

The staff of the department have been persistently working at the methodical providing of educational process.

The synopses of lectures, practicums and methodic manuals in all the main courses delivered at the department have been published. They were written by P. M. Hudyvok, V. S. Drobotenko, E. S. Drobotenko, Y. Y. Pohoriliak, S. S. Poliak, V. P. Rudko, V. F. Barannyk, O. A. Kyryliuk, I. Y. Shulla, I. V. Shapochka, O. A. Tylyshchak and N. V. Yurchenko. The methodical providing of educational process is being constantly renewed. The Department has one more important function – it is responsible for the vocational training of the students of the Mathematics Faculty as future school teachers. Special courses on Mathematics teaching at school are provided to this effect.

N.Drabov

14.10.2015

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