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On Rusakov’s n -ary r s -groups

Wiesław Aleksander DudekZoran Stojaković — 2001

Czechoslovak Mathematical Journal

Properties of n -ary groups connected with the affine geometry are considered. Some conditions for an n -ary r s -group to be derived from a binary group are given. Necessary and sufficient conditions for an n -ary group < θ , b > -derived from an additive group of a field to be an r s -group are obtained. The existence of non-commutative n -ary r s -groups which are not derived from any group of arity m < n for every n 3 , r > 2 is proved.

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