Geodesic
The free abelian $n$-ary groups defined by the cyclic groups
Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 68-76

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We give a complete description of the $n$-ary groups, which are free in the class of abelian $n$-ary groups defined by the cyclic groups and their automorphism groups. 
@article{CHEB_2011_12_2_a8,
     author = {V. M. Kusov and N. A. Shchuchkin},
     title = {The free abelian $n$-ary groups defined by the cyclic groups},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {68--76},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a8/}
}
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V. M. Kusov; N. A. Shchuchkin. The free abelian $n$-ary groups defined by the cyclic groups. Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 68-76. http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a8/