Geodesic
Congruences of finite multi-base universal algebras isomorphic to $n$-ary groups derived from groups
Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 131-142 
I. G. Shaposhnikov. Congruences of finite multi-base universal algebras isomorphic to $n$-ary groups derived from groups. Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 131-142. http://geodesic.mathdoc.fr/item/MVK_2022_13_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The homomorphism of a multi-base universal algebra to a multi-base universal algebra will be called an $mb$-homomorphism, and the corresponding congruences will be called $mb$-congruences. A description is obtained of $mb$-congruences of finite multi-base universal algebras, $mb$-isomorphic to $n$-ary groups derived from groups, that is, admitting representation in the form of a sequential application of the operation of some group. In particular, this class includes universal algebras for which the Gluskin – Hosszu theorem and its analogues are valid for $n$-ary operations.

[1] Gorchinskii Yu.N., “O gomomorfizmakh mnogoosnovnykh universalnykh algebr v svyazi s kriptograficheskimi primeneniyami”, Trudy po diskretnoi matematike, 1 (1997), 67–84 | MR

[2] Shaposhnikov I.G., “O kongruentsiyakh konechnykh mnogoosnovnykh universalnykh algebr”, Diskretnaya matematika, 11:3 (1999), 46–62

[3] Galmak A.M., $n$-arnye gruppy, v. 1, GGU im. F. Skoriny, Gomel, 2003, 196 pp.

[4] Gluskin L. M., “Pozitsionnye operativy”, Matematicheskii sbornik, 68(110):3 (1965), 444–472

[5] Hosszú M., “On the explicit form of $n$-group operations”, Publ. Math., 10 (1964), 88–92 | MR

[6] Belousov V.D., $n$-arnye kvazigruppy, Shtiintsa, Kishinev, 1972, 225 pp.

[7] Malyshev F.M., “Teorema Posta–Gluskina–Khossu dlya konechnykh $n$-kvazigrupp i samoinvariantnye semeistva podstanovok”, Matematicheskii sbornik, 207:2 (2016), 81–92

[8] Artamonov V.A., “O shreierovykh mnogoobraziyakh $n$-grupp i $n$-polugrupp”, Trudy seminara I.G. Petrovskogo, 5, 1979, 193–203

[9] Janeva B., “Congruences on $n$-groups”, Vat. Bilten (Skopje), 45 (1995), 85–90 | MR

[10] Usan J., “Congruences of $n$-groups and of associates Hosszú–Gluskin algebras”, Nove Sad J. Math., 28:2 (1998), 91–108 | MR

[11] Galmak A.M., Kongruentsii poliadicheskikh grupp, Belaruskaya navuka, Minsk, 1999, 182 pp.

[12] Galmak A.M., “O smezhnykh klassakh kongruentsii poliadicheskoi gruppy”, Vest. Viteb. gos. un-ta, 2002, no. 2, 114–118 | MR

[13] Usan J., “Note on congruences on $n$-ary group”, Mathematika Moravica, 6 (2002), 131–135 | DOI | MR

[14] Gal'mak A.M., “On congruences of $n$-ary group”, East Asian Math. J., 21:2 (2002), 241–248 | MR

[15] Khodabandeh H., Shahryari M., “On the automorphisms and representations of polyadic groups”, Comm. Algebra, 40:6 (2012), 2199–2212 | DOI | MR

[16] Shahryari M., “Representations of finite polyadic groups”, Comm. Algebra, 40:5 (2012), 1625–1631 | DOI | MR

[17] Khodabandekh Kh., Shakhriyari M., “Prostye poliadicheskie gruppy”, Sib. matem. zh., 55:4 (2014), 898–911 | MR

[18] Shaposhnikov I.G., “O gomotopiyakh konechnykh $n$-kvazigrupp”, Kvazigruppy i ikh sistemy, Matematicheskie issledovaniya, 113, Shtiintsa, Kishinev, 1990, 124–128

[19] Borisenko V.V., “Neprivodimye $n$-kvazigruppy na konechnykh mnozhestvakh sostavnogo poryadka”, Kvazigruppy i ikh sistemy, Matematicheskie issledovaniya, 51, Shtiintsa, Kishinev, 1979, 38–42

[20] Kostrikin A.I., Vvedenie v algebru, v. III, Osnovnye struktury, 3-e izd., Fizmatlit, M., 2004, 272 pp.