On n-ary subgroups of a special n-ary group
2010jcz | Galmak A.M., Vorobev G.N., Balan V.D.  // Mogilev State University of Food Technology, Mogilev, Belarus; Polytechnical University of Bucharest, Bucharest, Romania, mgup@mogilev.by, vbalan@mathem.pub.ro

We consider the Cartesian power An−1 (n ≥ 3) of the group A, which admits a subgroup B such that the factor group A/B is cyclic and with its order dividing n − 1. On An−1 we construct an n−ary group structure < An−1, [ ]n,n−1 > with its operation similar to the one defined by E. Post for n−ary permutations. This structure is shown to admit semi-invariant - but generally not invariant, n−ary subgroups.

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