On Rusakov's n-ary rs-Groups

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Properties of n-ary groups connected with the affine geometry are considered. Some conditions for an n-ary rs-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 rs-group are obtained. The existence of non-commutative n-ary rs-groups which are not derived from any group of arity m<n for every n≥3, r>2 is proved.

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