Sets of permutations that generate the symmetric group pairwise

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:113

Article

Blackburn, Simon R.

关键词: alternating group;    symmetric group;    subgroup covering;    local lemma;   

DOI  :  10.1016/j.jcta.2006.01.001

来源: Elsevier

【 摘 要 】

The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of 2(n-1) permutations that pairwise generate the symmetric group S, There is no set of 2(n-1) + 1 permutations having this property. For all sufficiently large integers n with n 2 mod 4, there exists a set of 2(n-2) even permutations that pairwise generate the alternating group A(n). There is no set of 2(n-2) + 1 permutations having this property. (c) 2006 Elsevier Inc. All rights reserved.

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