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. 
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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/

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