Sokhatsky Fedir Mykolayovych

Education: Vinnytsia State Pedagogical Institute (specialty – mathematics, 1978), postgraduate studies at the Institute of Mathematics of the Central Scientific Center of the Academy of Sciences of the MRSR in 1986, doctoral studies at the Taras Shevchenko National University of Kyiv. Academy of Public Administration under the President of Ukraine, 2000.

Scientific degree: Doctor of sciences in physics and mathematics (01.01.06 algebra and number theory) (doctoral thesis "Associates and factorization of multi-place operations", 2008)

Scientific title: Docent.

Position: Senior Research Fellow.

In Institute: from 2024.

Scientific profiles

ORCID: https://orcid.org/0000-0003-4969-5651

Research interests: theory of binary and multi-place invertible functions (in particular, quasigroup operations) and functional equations over them. Mathematical foundations of cryptology.

Main scientific results:

1. A system of axioms of the class (2,n)-semigroups of n-ary operations has been found (V.S. Trokhymenko's problem).

2. The complete decompositions of k-valued logic functions, which depend strongly on each variable, are almost identical. (A.V. Kuznetsov's problem).

3. The functional associativity equation and the generalized functional associativity equation on strongly dependent multiary functions of k-valued logic has been solved.

4. A complete dependence between the identities that determine the associativity of multi-valued operations has been found (V.D. Belousov's problem).

5. It was proved that commutative IP loops are isomorphic if they are isotopic.

6. New mathematical foundations for asymmetric cryptoalgorithms based on multi-operations were constructed.

7. The laws of parastrophic symmetry in quasigroup theory are described.

Major publications:

1. F. M. Sokhatsky, H. V. Krainichuk, V. A. Luzhetsky, Canonical and matrix figuration of quasigroups of the fourth order. Prykl. Probl. Mekh. Mat., Issue 22, 95–105 (2024) (in Ukrainian), https://doi.org/10.15407/apmm2024.22.95-105

2. Sokhatsky, F.M., Lutsenko, A.V., Fryz, I.V. Construction of Quasigroups with Invertibility Properties. J. Math. Sci. 279, 115–132 (2024). DOI: https://doi.org/10.1007/s10958-024-06999-0

3. Iryna Fryz, Fedir Sokhatsky, “Construction of medial ternary self-orthogonal quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 3, 41–55 DOI: https://doi.org/10.56415/basm.y2022.i3.p41

4. Fedir Sokhatsky, Alla Lutsenko, Classification of quasigroups according to directions of translations II. Comment. Math. Univ. Carolin. 62,3 (2021) 309 –323. (Scopus,Q3) DOI: 10.14712/1213-7243.2021.021

5. F. M. Sokhatsky, H. V. Krainichuk, and V. A. Sydoruk Semi-lattice of varieties of quasigroups with linearity Algebra and Discrete Mathematics, 31 (2021). Number 2, pp. 261–285 DOI:10.12958/adm1748 https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1748/pdf (Scopus, Q4)

6. Tarasevych A., Sokhatsky F. Ternary universal loops satisfying quadratic identities of the length three. The scientific heritage (Budapest, Hungary). VOL 1, No 59 (2021). P.3-10. DOI: 10.24412/9215-0365-2021-59-1-3-10

7. Sokhatsky F.M., Lutsenko A.V., Fryz I.V. Constructing quasigroups with invertibility property. Math. Methods and Physic.-Mech. Fields, 64, (2021), No.4 (in Ukrainian).

8. Fedir Sokhatsky, Alla Lutsenko, Classification of quasigroups according to directions of translations I Comment. Math. Univ. Carolin. 61,4 (2020) 567–579. (Scopus, Q4) DOI: 10.14712/1213-7243.2021.002

9. F. M. Sokhatsky, A. V. Tarasevych, “On ternary quasigroup quadratic identities of the small length,” Appl. probl. mech. and math., 18, 150–161 (2020), https://doi.org/10.15407/apmm2020.18.150-161

10. F. M. Sokhatsky, A. V. Tarasevych, Classification of generalized ternary quadratic quasigroup functional equations of the length three, Carpathian Math. Publ. 2019, 11 (1), 179-192. (Scopus, Q2) https://doi.org/10.15330/cmp.11.1.179-192

11. Sokhatsky F., About orthogonality of multiary operations, Bulletin of Donetsk National University. Series A: Natural Sciences, 1-2 (2018), P. 49-55. DOI: http://dx.doi.org/10.31558/1817-2237.2018.1-2.3

12. Halyna Krainichuk, Fedir Sokhatsky, “Solution and full classification of generalized binary functional equations of the type (3;3;0)”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 2, 41–53, Scopus. (Scopus, Q4)

13. Sokhatsky F., Lutsenko A. The bunch of varieties of inverse property quasigroups, Bulletin of Donetsk National University.Series A: Natural Sciences, 1-2 (2018) , P. 56-69. DOI: http://dx.doi.org/10.31558/1817-2237.2018.1-2.4

14. Sokhatsky F., Pirus Y. Classification of ternary quasigroups according to their parastrophic symmetry groups, I, Bulletin of Donetsk National University. Series A: Natural Sciences, 1-2 (2018) , P. 70-82. DOI: http://dx.doi.org/10.31558/1817-2237.2018.1-2.5

15. Sokhatsky F., Factorization of medial and abelian algebras // Bulletin of Donetsk National University. Series A: Natural Sciences. — 2017. – No. 1-2. ¬-P. 84–96. DOI: https://doi.org/10.31558/1817-2237.2017.1-2.7

16. Sokhatsky F., Krainichuk H., Tarasevych A. A classification of generalized functional equations on ternary quasigroups // Bulletin of Donetsk National University. Series A: Natural Sciences. — 2017. – No. 1-2. ¬-P. 97–107. DOI: https://doi.org/10.31558/1817-2237.2017.1-2.8

17. Fedir Sokhatsky, Olena Tarkovska, On linearity of isotopes of abelian groups.// Bulletin of Donetsk National University. Series A: Natural Sciences. — 2017. – No. 1-2. ¬-P. 108–118. DOI: https://doi.org/10.31558/1817-2237.2017.1-2.9

18. Fryz I.V., Sokhatsky F.M. Block composition algorithm for constructing orthogonal n-ary operations // Discrete mathematics, 2017 Scopus Q1, індекс SNIP= 1,040)

19. Sokhatsky Fedir M. On pseudoisomorphy and distributivity of quasigroups Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2016, No. 2(81), 125–142.

20. Sokhatsky F. M. Symmetry in quasigroup theory, Bull. of DonNU. Ser. A. Natural Sciences, 2016, No. 1–2, 70–83.

21. Fedir M. Sokhatsky, Iryna V. Fryz, Invertibility criterion of composition of two multiary quasigroups, Comment. Math. Univ. Carolin. 53,3(2012) 429-445. (Scopus, Q4)

22. Fedir M. Sokhatsky, Halyna V. Krainichuk Solution of distributive-like quasigroup functional equations Commentationes Mathematicae Universitatis Carolinae, Vol. 53 (2012), No. 3, 447-459 (Scopus, Q4)

23. Sokhatsky F.M. About mediality of universal algebras and cross group isotopes.// Reports of the National Academy of Sciences of Ukraine. — 2006. — no 11. — P. 29-35

24. Sokhatsky F.M. About cross isotopy and cross isomorphism. Proceedings of IAMM of NASU. Vyp. 11, 2005, с.23-33

25. F.M. Sokhatsky, O.V. Yurevych, “On Commutativity and Mediality of Polyagroup Cross Isomorphs”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, no. 3, 141–152.

26. Sokhats’kyi, F.M. On the classification of functional equations on quasigroups. Ukr Math J 56, 1499–1508 (2004). https://doi.org/10.1007/s11253-005-0129-3

27. Fedir M. Sokhatsky Commutation of operations and its relationship with Menger and Mann superpositions. Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 153-176, DOI: https://doi.org/10.7151/dmgaa.1082

28. Sokhatsky F.M. New clone of operations and their abstract characterization. Scientific Journal of Drahomanov Ukrainian State University. Series 1. Physical and mathematical sciences. – Kyiv: Drahomanov Ukrainian State University, 2004, №5, С. 97-110.

29. Sokhatsky F.M. On Dudek's problems on the skew operation in poliadic groups. // East Asian Math. J. 19 (2003), N1, pp.63-71.

30. Sokhats'kyi F. M. Abstract Characteristic of the Class of Unitary Positional Algebras of Operations. // Ukrainian Mathematical Journal, 2002, (Kluwer Academic Publishers-Plenum Publishers) - Vol. 54, Iss: 7, pp 1159-1168

31. Sokhatsky F.N. Kirnasovsky O.E. Canonical decompositions of multiary isotopes of groups. Izvestia of the Gomel State University named after F. Skoryny, 2001, N3(6).- P.87-96.

32. Harvadsky V.S., Kulyk V.T., Sokhatsky F.N. Strong congruences of partial universal algebras.// Izvestia of the Gomel State University named after F. Skoryny, 2001, N3(6).- P. 67-76.

33. Sokhatsky F.N., Yurevych O.V., Koval’ R.F. Обратимые выборки и обратимые элементы делимых изотопов моноидов. Izvestia of the Gomel State University named after F. Skoryny, 2001, N3(6).- P. 97-109.

34. Sokhatsky F.M. Some linear conditions and their application to describing group isotopes. Quasigroups and Related Systems. 6 (1999), 43–59.

35. Sokhatsky F.M.,Yurevych O., Invertible elements in associates and semigroups. 2 Quasigroups and Related Systems 6 (1999), 61-70.

36. Sokhatsky F.M. Invertible elements in associates and semigroups.I. // Quasigroups and Related Systems. 5 (1998), 53–68.

37. Sokhatsky F.M. On the associativity of multiplace operations. // Quasigroups and Related Systems. 4 1997, 51-56.

38. F. N. Sokhatsky: On polyadic groups, (Russian), Sovriemiennaya algebra 2(22) (1997), 79 − 94.

39. Sokhatsky F.M. On the associativity of multiplace operations. Quasigroups and Related Systems. 4 1997, 51-56.

40. SokhatskiiF.N. On Isotopes of Groups. III. Ukrainian Mathematical Journal. Vol.48, No.2, 1996. P.283-293.

41. Sokhatsky F.M. The Deepest Repetition-Free Decompositions of Non-Singular Functions of Finite Valued Logics. // Proceeding of The Twenty-Sixth International symposium on Multiple-Valued Logic (May 29–31, 1996, Santiago de Compostela, Spain), P.279–282.

42. F. M. Sokhatsky: About classes of polyagroups, In "Algebraicheskie issledovania", Inst. Mat. NAN Ukrainy, Kyiv 1996, 114−131.

43. Sokhatskii F.N. On Isotopes of Groups.I. Ukrainian Mathematical Journal. Vol.47, No.10, 1995. P.1585-1598.

44. Sokhatskii F.N. On Isotopes of Groups.II. Ukrainian Mathematical Journal. Vol.47, No.12, 1995. P.1935-1948.

45. Sokhatsky F.M. On superassociative group isotopes. Quasigroups and Related Systems, №1, v.2.– Chishinau.–1995.– P.101–119.

46. Sokhatsky F.M., Syvakivsky P.B. On linear isotopes of cyclic groups // Quasigroups and Related Systems, №1 (1), v.1.– 1994.– P.66–76.

47. F. M. Sokhatsky: About associativity of multiplace operations, (Russian), Diskretnaya matematyka 4 (1992), 66 − 84.

48. Sokhatsky F.N. Multiary divisible quasigroups with invertible property. Quasigroups and their systems: Math. issled. – Kishinev: Stiintsa, 1990., P.89– 99.

49. Sokhatsky F.N. Positional algebra. Belousov’s algebras. Quasigroups: Math. issled. – Kishinev: Stiintsa.– 1987., Vyp.95., P.101–120.

50. Sokhatsky F.N. About decompositions of n-ary quasigroups. // Second International Symposium "n-Ary structures" (Varna'83)/ Proseedings.–Sofia.–1985, P. 33-47.

51. Sokhatsky F.N. Generalization of two Belousov’s theorem for the strong dependence functions of k-valued logics. Math. issled. – Kishinev: Stiintsa.– 1983., Vyp.71., P.104– 117.

52. Sokhatsky F.N. About positiona algebras.// Quasigroups and Latin squares: Math. issled. – Kishinev: Stiintsa.– 1985., Vyp.83., P.105– 115.

53. Sokhatsky, F. M. (1982). An abstract characterization of (2,n)-semigroups of n-ary operations. Mat. Issled.65:132–139 (Russian)

Phone service: (032) 258 96 24

E–mail: fmsokha@ukr.net, fmsokha@gmail.com