Geodesic
On parallel straight lines designated on an $n$-ary group
Problemy fiziki, matematiki i tehniki, no. 4 (2012), pp. 54-57.

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

In the paper the other approach to the notion of the parallelogram on the $n$-ary group is presented. Traditionally a parallelogram on an $n$-ary group is considered as four points satisfying the determined identity. Here the parallelogram is considered as two pairs of parallel straight lines. These two approaches are proved to be equivalent.
Keywords: $n$-ary group, inverse sequence, neutral sequence, parallel straight line, parallelogram. 
@article{PFMT_2012_4_a9,
     author = {Yu. V. Kravchenko},
     title = {On parallel straight lines designated on an $n$-ary group},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {54--57},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2012_4_a9/}
}
TY  - JOUR
AU  - Yu. V. Kravchenko
TI  - On parallel straight lines designated on an $n$-ary group
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2012
SP  - 54
EP  - 57
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2012_4_a9/
LA  - ru
ID  - PFMT_2012_4_a9
ER  - 
%0 Journal Article
%A Yu. V. Kravchenko
%T On parallel straight lines designated on an $n$-ary group
%J Problemy fiziki, matematiki i tehniki
%D 2012
%P 54-57
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2012_4_a9/
%G ru
%F PFMT_2012_4_a9
Yu. V. Kravchenko. On parallel straight lines designated on an $n$-ary group. Problemy fiziki, matematiki i tehniki, no. 4 (2012), pp. 54-57. http://geodesic.mathdoc.fr/item/PFMT_2012_4_a9/

[1] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970, 392 pp. | MR

[2] A. G. Kurosh, Lektsii po obschei algebre, Nauka, M., 1973, 399 pp.

[3] M. Kholl, Teoriya grupp, IL, M., 1962, 468 pp.

[4] S. A. Chunikhin, Podgruppy konechnykh grupp, Nauka i tekhnika, Minsk, 1964, 158 pp. | MR | Zbl

[5] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 267 pp. | MR | Zbl

[6] L. A. Shemetkov, A. N. Skiba, Formatsii algebraicheskikh sistem, Nauka. Gl. red. fiz.-mat. lit., M., 1989, 256 pp. | MR

[7] S. F. Kamornikov i dr., Podgruppovye funktory v teorii klassov konechnykh grupp, Preprint, Gomelskii gosudarstvennyi universitet imeni F. Skoriny, Gomel, 2001, 237 pp.

[8] W. Dornte, “Untersuchunden uber einen verall”, Math. Z., 29 (1928), 119 | MR

[9] E. L. Post, “Polyadic groups”, Trans. Amer. Math. Soc., 48:2 (1940), 208–305 | DOI | MR

[10] S. A. Chunikhin, “K teorii neassotsiativnykh $n$-grupp s postulatom K”, Dokl. AN SSSR, 48:1 (1945), 7–10

[11] S. A. Rusakov, Algebraicheskie $n$-arnye sistemy: Silovskaya teoriya $n$-arnykh grupp, Navuka i tekhnika, Minsk, 1992, 264 pp.

[12] A. M. Galmak, Teoremy Posta i Gluskina–Khossu, GGU im. F. Skoriny, Gomel, 1997, 82 pp.

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

[14] S. F. Kamornikov, Yu. V. Kravchenko, “Funktory Gashyutsa”, Voprosy algebry (Gomel), 1999, no. 15, 37–40 | Zbl

[15] Yu. V. Kravchenko, Regulyarnye filtruyuschie podgruppovye funktory, Preprint No 12, Gomelskii gos. un-t im. F. Skoriny, Gomel, 2002, 10 pp.

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

[17] A. Yu. Olshanskii, Geometriya opredelyayuschikh sootnoshenii v gruppakh, Nauka, M., 1989, 448 pp. | MR

[18] Yu. I. Kulazhenko, “Geometriya parallelogrammov”, Voprosy algebry i prikladnoi matematiki, Sb. nauch. tr., ed. S. A. Rusakov, Gomel,, 1995, 47–64

[19] Yu. I. Kulazhenko, “Simmetriya, shestiugolniki i poluabelevost $n$-arnykh grupp”, Izvestiya Gomelskogo gosudarstvennogo universiteta imeni F. Skoriny, 2008, no. 2 (47), 99–106