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On generation of the symmetric or the alternating group by two cycles

Volume 150 / 2017

Czesław Bagiński, Grzegorz Gromadzki Colloquium Mathematicum 150 (2017), 161-174 MSC: Primary 20B30; Secondary 20B25, 20B35. DOI: 10.4064/cm7090-10-2016 Published online: 30 June 2017

Abstract

We study the question which pairs of cycles generate the alternating or the symmetric group. We give some sufficient conditions for that, which are also frequently necessary. Furthermore, we also characterize a certain class of involutive automorphisms of such groups. The paper has a combinatorial character but the problems are motivated by geometry.

Authors

  • Czesław BagińskiFaculty of Computer Science
    Białystok University of Technology
    15-351 Białystok, Poland
    e-mail
  • Grzegorz GromadzkiInstitute of Mathematics
    University of Gdańsk
    80-952 Gdańsk, Poland
    e-mail

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