Abstract
We show that for n ≥ 3, the clone of the dihedral group \({D_{{2}^{n}}}\) is determined by the k-ary algebraic relations, where k = 2n−1. Further, we show that there does not exist a finite integer k > 0 such that for all finite groups G, the k-ary algebraic relations of G determine the clone of G.
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Presented by E. Kiss.
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Shaw, J. Commutator relations and the clones of finite groups. Algebra Univers. 72, 29–52 (2014). https://doi.org/10.1007/s00012-014-0287-y
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DOI: https://doi.org/10.1007/s00012-014-0287-y