Abstract
We prove that the symmetric group S r of prime degree r≥17 is recognizable by its element order set. A test for recognizability is obtained for the symmetric group S r+1 with r≥17 prime.
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Zavarnitsine, A.V. Recognition by the Set of Element Orders of Symmetric Groups of Degree r and r+1 for Prime r. Siberian Mathematical Journal 43, 808–811 (2002). https://doi.org/10.1023/A:1020142420831
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DOI: https://doi.org/10.1023/A:1020142420831