Bijectivity of the skew map in $n$-groups
Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 106-112.

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

A number of problems connected with the skew map $h\colon x\to\bar{x}$ in an $n$-group is considered. In this paper some $n$-groups where $h\colon x\to\bar{x}$ and ${}^{(t)}\colon x\to x^{(t)}$ are automorphisms or bijective maps are indicated.
@article{TIMB_2008_16_1_a18,
     author = {N. A. Schuchkin},
     title = {Bijectivity of the skew map in $n$-groups},
     journal = {Trudy Instituta matematiki},
     pages = {106--112},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a18/}
}
TY  - JOUR
AU  - N. A. Schuchkin
TI  - Bijectivity of the skew map in $n$-groups
JO  - Trudy Instituta matematiki
PY  - 2008
SP  - 106
EP  - 112
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a18/
LA  - ru
ID  - TIMB_2008_16_1_a18
ER  - 
%0 Journal Article
%A N. A. Schuchkin
%T Bijectivity of the skew map in $n$-groups
%J Trudy Instituta matematiki
%D 2008
%P 106-112
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a18/
%G ru
%F TIMB_2008_16_1_a18
N. A. Schuchkin. Bijectivity of the skew map in $n$-groups. Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 106-112. http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a18/

[1] Rusakov S.A., Algebraicheskie $n$-arnye sistemy, Navuka i tekhnika, Minsk, 1992

[2] Galmak A.M., $n$-Arnye gruppy. Chast I, Gomelskii gos. un-t im. F. Skoriny, Gomel, 2003

[3] Kurosh A.G., Obschaya algebra. Lektsii 1969–1970 uch. goda, Nauka, M., 1974 | MR

[4] Dudek W.A., Glasek K., Gleichgewicht B., “A note on the axioms of $n$-groups”, Coll. Math. Soc. J. Bolyai 29: Universal Algebra (Esztergom, Hungaru, 1977), North-Holland, Amsterdam, 1982, 195–202 | MR

[5] Dudek W.A., “Remarks on $n$-groups”, Demonstratio Math., 13 (1980), 165–181 | MR | Zbl

[6] Gleichgewicht B., Schuchkin K., “Remarks on $n$-groups as abstract algebras”, Coll. Math., 17 (1967), 209–219 | MR | Zbl

[7] Dudek W.A., “On $n$-ary group with only one skew element”, Radovi Matematicki (Sarajevo), 6 (1990), 171–175 | MR | Zbl

[8] Dudek W.A., “On some old and new problems in $n$-ary groups”, Quasigroups and Related Systems, 8 (2001), 15–36 | MR | Zbl

[9] Schuchkin N.A., “Skew endomorphism in $n$-ary groups”, Quasigroups and Related Systems, 14 (2006), 209–218

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

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

[12] Galmak A.M., “$n$-Arnye analogi khollovskikh podgrupp”, Vesnik MDU im. A.A. Kulyashova, 2001, no. 2–3 (9), 117–123

[13] Galmak A.M., “Khollovy kongruentsii $n$-arnykh grupp”, Izv. GGU im. F. Skoriny, 2004, no. 6 (27), 93–100

[14] Dudek I.M., Dudek W.A., “On skew elements in $n$-groups”, Demonstratio Math., 14 (1981), 827–833 | MR | Zbl