On recursive 1-differentiability of the quasigroup prolongations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 102-109.

Voir la notice de l'article provenant de la source Math-Net.Ru

The recursive differentiability of finite binary quasigroups is investigated. We consider the Bruck and Belousov constructions of prolongation of finite quasigroups and give necessary and sufficient conditions when such prolongations are recursively 1-differentiable.
@article{BASM_2023_2_a8,
     author = {Parascovia Syrbu and Elena Cuzne\c{t}ov},
     title = {On recursive 1-differentiability of the quasigroup prolongations},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {102--109},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2023_2_a8/}
}
TY  - JOUR
AU  - Parascovia Syrbu
AU  - Elena Cuzneţov
TI  - On recursive 1-differentiability of the quasigroup prolongations
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2023
SP  - 102
EP  - 109
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2023_2_a8/
LA  - en
ID  - BASM_2023_2_a8
ER  - 
%0 Journal Article
%A Parascovia Syrbu
%A Elena Cuzneţov
%T On recursive 1-differentiability of the quasigroup prolongations
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2023
%P 102-109
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2023_2_a8/
%G en
%F BASM_2023_2_a8
Parascovia Syrbu; Elena Cuzneţov. On recursive 1-differentiability of the quasigroup prolongations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 102-109. https://geodesic-test.mathdoc.fr/item/BASM_2023_2_a8/

[1] R. H. Bruck, “Some results in the theory of quasigroups”, Trans. Amer. Math. Soc., 55 (1944), 19–52 | DOI | MR | Zbl

[2] V. Belousov, “Extensions of quasigroups”, Izv. Akad. Nauk Mold. SSR, Ser. Fiz. Tekh. Mat. Nauk, 1967, no. 8, 3–24 (in Russian) | MR | Zbl

[3] E. Couselo, S. Gonsales, V. Markov, A. Nechaev, “Recursive MDS codes and recursively dif ferentiable quasigroups”, Discrete Math. Appl., 8:3 (1998), 217–245 | DOI | MR | Zbl

[4] V. Markov, A. Nechaev, S. Skazhenik, E. Tveritinov, “Pseudogeometries with clusters and an example of a recursive $[4, 2, 3]_{42}$-code”, J. Math. Sci., 163:5 (2009), 563–571 | DOI | MR | Zbl

[5] P. Syrbu, E. Cuzneţov, “On recursively differentiable k quasigroups”, Bul. Acad. Sţiinţe Re pub. Mold., Mat., 2022, no. 2(99), 68–75 | MR

[6] V. Izbash, P. Syrbu, “Recursively differentiable quasigroups and complete recursive codes”, Commentat. Math. Univ. Carol., 45:2 (2004), 257–263 | MR | Zbl

[7] A. D. Keedwell, J. Denes, Latin Squares and their Applications, 2nd ed., Elsevier, Amsterdam, 2015, xiv+424 pp. | MR | Zbl