Abstract
Let G be a finite permutation group of degree n, and let d = 2 if G = Sym(3), d = [n/2] otherwise. We prove that there exist d elements g 1, . . . , g d in G with the property that \({G=\langle g_1^{x_1},\ldots,g_d^{x_d}\rangle}\) for every choice of \({(x_1,\ldots,x_d)\in G^d}\).
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The research was partially supported by GNSAGA (INdAM).
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Detomi, E., Lucchini, A. Invariable generation of permutation groups. Arch. Math. 104, 301–309 (2015). https://doi.org/10.1007/s00013-015-0749-2
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DOI: https://doi.org/10.1007/s00013-015-0749-2