Abstract
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 \(\left\langle {\theta ,b} \right\rangle \)-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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Dudek, W.A., Stojakovic, Z. On Rusakov's n-ary rs-Groups. Czechoslovak Mathematical Journal 51, 275–283 (2001). https://doi.org/10.1023/A:1013726412996
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DOI: https://doi.org/10.1023/A:1013726412996