Geodesic
Semicommutativity and properties of vectors in $n$-ary groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 142-147 Cet article a éte moissonné depuis la source Math-Net.Ru

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We establish new criteria for the semicommutativity of an $n$-ary group expressed in terms of properties of vectors and symmetric points.
Keywords: $n$-ary group, vector of an $n$-ary group, semicommutative $n$-ary group, symmetric points. 
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Yu. I. Kulazhenko. Semicommutativity and properties of vectors in $n$-ary groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 142-147. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a13/

[1] Dörnte W., “Untersuchungen einen verallgemeinerten Gruppenbegriff”, Math. Z., 29 (1928), 1–19 | DOI | MR | Zbl

[2] Prüfer H., “Theorie der abelshen Gruppen. I. Grundeigenschaften”, Math. Z., 20 (1924), 165–187 | MR | Zbl

[3] Post E. L., “Polyadic groups”, Trans. Amer. Math. Soc., 48:2 (1940), 208–350 | DOI | MR | Zbl

[4] Rusakov S. A., Nekotorye prilozheniya teorii $n$-arnykh grupp, Belaruskaya navuka, Minsk, 1998, 182 pp.

[5] Vakarelov D., “Ternarni grupi”, Godishnik Sofiisk. un-ta. Mat. fak-t, 61 (1966–1967), 71–105 (1968) | MR

[6] Dudek W. A., “Ternary quasigroups connected with the affine geometry”, Algebras Groups Geom., 16:3 (1999), 329–354 | MR | Zbl

[7] Dudek W. A., Stojakovic N. A., “On Rusakov's $n$-ary $rs$-groups”, Czechoslovak Math. J., 51(126):2 (2001), 275–283 | DOI | MR | Zbl

[8] Glazek K., Gleichgewicht B., “Abelian groups”, Proc. Congr. Math. Soc. Universal Algebra (Esztergom, Hungary), Math. Soc. J. Bolyai, 29, 1977, 321–329 | MR

[9] Baer R., Linear algebra and projective geometry, Academic Press, New York, 1952, 318 pp. | MR | Zbl

[10] Branzei D., “Structures affines et operations ternaries”, Sti. Univ. Iasi. Sect. IA Mat., 23 (1977), 33–38 | MR | Zbl

[11] Kulazhenko Yu. I., “Semi-cummutativity criteria and self-coincidence of elements expressed by vectors properties of $n$-ary groups”, Algebra and Discrete Math., 9:2 (2010), 98–107 | MR | Zbl

[12] Galmak A. G., Kulazhenko Yu. I., “O poluabelevykh, kommutativnykh i affinnykh $n$-arnykh gruppakh”, Algebra i teoriya chisel. Sovremennye problemy i prilozheniya, Tez. dokl. Kh Mezhdunar. konf., Volgograd, 2012, 20–23

[13] Kurosh A. G., Obschaya algebra, Lektsii 1969/70 uchebnogo goda, Nauka, M., 1974, 160 pp. | MR

[14] Dudek W. A., “Varieties of polyadic groups”, Filomat, 9:3 (1995), 657–674 | MR | Zbl

[15] Rusakov S. A., Algebraicheskie $n$-arnye sistemy. Silovskaya teoriya $n$-arnykh grupp, Belaruskaya navuka, Minsk, 1992, 264 pp.

[16] Kulazhenko Yu. I., “Vektory i kriterii poluabelevosti $n$-arnykh grupp”, Problemy fiziki, matematiki i tekhniki, 2011, no. 1(6), 65–68 | Zbl