Sets of permutations that generate the symmetric group pairwise |
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| Authors: | Simon R Blackburn |
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| Institution: | Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK |
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| Abstract: | The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of 2n−1 permutations that pairwise generate the symmetric group Sn. There is no set of 2n−1+1 permutations having this property. For all sufficiently large integers n with n≡2mod4, there exists a set of 2n−2 even permutations that pairwise generate the alternating group An. There is no set of 2n−2+1 permutations having this property. |
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| Keywords: | Alternating group Symmetric group Subgroup covering Local lemma |
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