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. 
@article{PFMT_2014_2_a7,
     author = {A. M. Gal'mak and N. A. Shchuchkin},
     title = {Cyclic $n$-ary groups and their generalizations},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {46--53},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_2_a7/}
}
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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/