Geodesic
Cyclic $n$-ary groups and their generalizations
Problemy fiziki, matematiki i tehniki, no. 2 (2014), pp. 46-53.

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The authors define and study $m$-semicyclic $n$-ary groups for any divisor $m-1$ of natural number $n-1$. The class of all $m$-semicyclic $n$-ary groups is included in the class of all $m$-semiabelian $n$-ary groups identified by E. Post. Moreover, the class of all $m$-semicyclic $n$-ary groups includes the class of all cyclic $n$-ary groups and belongs to the class of all semicyclic $n$-ary groups. New criteria of cyclicity for $n$-ary group and for $m$-semicyclicity of $n$-ary group formulated by one of the subgroups of the universal covering group of Post are determined.
Keywords: $n$-ary group, cyclic group, semicyclic group, $m$-semicyclic group. 
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A. M. Gal'mak; N. A. Shchuchkin. Cyclic $n$-ary groups and their generalizations. Problemy fiziki, matematiki i tehniki, no. 2 (2014), pp. 46-53. http://geodesic.mathdoc.fr/item/PFMT_2014_2_a7/

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

[2] A. M. Galmak, $n$-Arnye gruppy, v. 1, GGU im. F. Skoriny, Gomel, 2003, 202 pp.

[3] A. M. Galmak, N. A. Schuchkin, “K teoreme Posta o smezhnykh klassakh”, XI Mezhdunar konf. «Algebra i teoriya chisel: sovremennye problemy i prilozheniya», tez. dokl. (Saratov, 10–16 sent. 2012), 39–40 | MR

[4] V. A. Artamonov, “Svobodnye $n$-gruppy”, Mat. zametki, 8:4 (1970), 499–507 | MR

[5] V. A. Artamonov, “O shraierovykh mnogoobraziyakh $n$-grupp i $n$-polugrupp”, Trudy seminara im. I. G. Petrovskogo, 5, 1979, 193–202 | MR

[6] S. A. Rusakov, Algebraicheskie $n$-arnye sistemy, Navuka i tekhnika, Mn., 1992, 245 pp.

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

[8] N. A. Schuchkin, “Polutsiklicheskie $n$-arnye gruppy”, Izvestiya GGU im. F. Skoriny, 2009, no. 3 (54), 186–194

[9] A. M. Galmak, G. N. Vorobev, “O teoreme Posta–Gluskina–Khossu”, Problemy fiziki, matematiki i tekhniki, 2013, no. 1 (14), 55–60