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.
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. 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
2. 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
3. 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
4. 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)
5. Tarasevych A., Sokhatsky
F. Ternary universal loops satisfying quadratic identities of the length three.
The scientific heritage (
6. 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).
7. 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
8. 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
9. 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
10. 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
11. 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)
12. 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
13. 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
14. 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
15. 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
16. Fedir Sokhatsky,
Olena Tarkovska, On linearity of isotopes of abelian
groups.// Bulletin of
17. Fryz I.V., Sokhatsky
F.M. Block composition algorithm for constructing
orthogonal n-ary operations // Discrete mathematics,
2017 Scopus Q1, ³íäåêñ SNIP= 1,040)
18. Sokhatsky Fedir M.
On pseudoisomorphy and distributivity
of quasigroups Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2016, No. 2(81),
125–142.
19. Sokhatsky F. M. Symmetry in quasigroup theory, Bull. of DonNU. Ser. A. Natural Sciences, 2016, No. 1–2, 70–83.
20. 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)
21. 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)
22. Sokhatsky F.M.
About mediality of universal algebras and cross group
isotopes.// Reports of the National Academy of Sciences of
23. Sokhatsky F.M.
About cross isotopy and cross isomorphism.
Proceedings of IAMM of NASU.
Vyp. 11, 2005, ñ.23-33
24. 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.
25. 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
26. 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
27. Sokhatsky F.M. New
clone of operations and their abstract characterization. Scientific Journal of
28. Sokhatsky F.M. On Dudek's problems on the skew operation in poliadic groups. // East Asian Math. J. 19 (2003), N1,
pp.63-71.
29. 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
30. Sokhatsky F.N. Kirnasovsky O.E. Canonical
decompositions of multiary isotopes of groups. Izvestia of the
31. 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.
32. Sokhatsky F.N., Yurevych O.V., Koval’ R.F. Îáðàòèìûå
âûáîðêè è îáðàòèìûå ýëåìåíòû äåëèìûõ èçîòîïîâ ìîíîèäîâ. Izvestia of the
33. Sokhatsky F.M. Some linear conditions and their application
to describing group isotopes. Quasigroups and Related
Systems. 6 (1999), 43–59.
34. Sokhatsky F.M.,Yurevych O., Invertible elements in associates and semigroups. 2 Quasigroups and
Related Systems 6 (1999), 61-70.
35. Sokhatsky F.M.
Invertible elements in associates and semigroups.I.
// Quasigroups and Related Systems. 5 (1998), 53–68.
36. Sokhatsky F.M. On
the associativity of multiplace
operations. // Quasigroups and Related Systems. 4
1997, 51-56.
37. F. N. Sokhatsky: On polyadic groups,
(Russian), Sovriemiennaya algebra 2(22) (1997), 79 −
94.
38. Sokhatsky F.M. On
the associativity of multiplace
operations. Quasigroups and Related Systems. 4 1997,
51-56.
39. SokhatskiiF.N. On
Isotopes of Groups. III. Ukrainian Mathematical Journal. Vol.48, No.2, 1996.
P.283-293.
40. 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.
41. F. M. Sokhatsky: About classes of polyagroups,
In "Algebraicheskie issledovania",
Inst. Mat.
42. Sokhatskii F.N. On
Isotopes of Groups.I. Ukrainian Mathematical Journal.
Vol.47, No.10, 1995. P.1585-1598.
43. Sokhatskii F.N. On
Isotopes of Groups.II. Ukrainian Mathematical
Journal. Vol.47, No.12, 1995. P.1935-1948.
44. Sokhatsky F.M. On superassociative group isotopes. Quasigroups
and Related Systems, ¹1, v.2.– Chishinau.–1995.–
P.101–119.
45. Sokhatsky F.M., Syvakivsky P.B. On linear
isotopes of cyclic groups // Quasigroups and Related
Systems, ¹1 (1), v.1.– 1994.– P.66–76.
46. F. M. Sokhatsky: About associativity of
multiplace operations, (Russian), Diskretnaya
matematyka 4 (1992), 66 − 84.
47. Sokhatsky F.N. Multiary divisible quasigroups
with invertible property. Quasigroups and their
systems: Math. issled. –
48. Sokhatsky F.N.
Positional algebra. Belousov’s algebras. Quasigroups: Math. issled.
–
49. Sokhatsky F.N.
About decompositions of n-ary quasigroups.
// Second International Symposium "n-Ary
structures" (
50. Sokhatsky F.N.
Generalization of two Belousov’s theorem for the
strong dependence functions of k-valued logics. Math. issled. –
51. Sokhatsky F.N. About
positiona algebras.// Quasigroups
and Latin squares: Math. issled.
–
52. 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