Geodesic
Analogues of Gluskin--Hossz\'{u} and Malyshev theorems for strongly dependent $n$-ary operations
Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 138-147

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The paper contains an extension of Malyshev theorem for $n$-ary quasigroups with a right or left weak invertibility property to the case of strongly dependent $n$-ary operations. As a corollary a new proof of Gluskin–Hosszú theorem for strongly dependent $n$-ary semigroups is obtained.
Keywords: $n$-ary groups, strongly dependent operations, weak invertibility. 
@article{DM_2018_30_2_a9,
     author = {A. V. Cheremushkin},
     title = {Analogues of {Gluskin--Hossz\'{u}} and {Malyshev} theorems for strongly dependent $n$-ary operations},
     journal = {Diskretnaya Matematika},
     pages = {138--147},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_2_a9/}
}
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A. V. Cheremushkin. Analogues of Gluskin--Hossz\'{u} and Malyshev theorems for strongly dependent $n$-ary operations. Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 138-147. http://geodesic.mathdoc.fr/item/DM_2018_30_2_a9/