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Permutation groups generated by cycles of fixed length

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Abstract

Combinatorial conditions on a set of cycles of fixed degree inS n are studied, so that they generateA n orS n . It is shown thatA n orS n is so generated if and only if a graph associated with the set of cycles is connected, provided two of the cycles satisfy certain, not too restrictive, criteria. As a corollary, the minimum number of cycles of degreem ≧ 2 that generateA n or Sn is determined.

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Authors and Affiliations

  1. Department of Mathematics Institute of Advanced Studies, The Australian National University, 2600, Canberra, ACT, Australia

    Marcel Herzog & K. B. Reid

  2. Department of Mathematics, Tel Aviv University, Tel Aviv, Israel

    Marcel Herzog & K. B. Reid

  3. Department of Mathematics, Louisiana State University, 70803, Baton Rouge, Louisiana, USA

    Marcel Herzog & K. B. Reid

Authors
  1. Marcel Herzog
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  2. K. B. Reid
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Herzog, M., Reid, K.B. Permutation groups generated by cycles of fixed length. Israel J. Math. 26, 221–231 (1977). https://doi.org/10.1007/BF03007644

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  • DOI: https://doi.org/10.1007/BF03007644

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