On generation of the symmetric or the alternating group by two cycles
Tom 150 / 2017
Colloquium Mathematicum 150 (2017), 161-174 MSC: Primary 20B30; Secondary 20B25, 20B35. DOI: 10.4064/cm7090-10-2016 Opublikowany online: 30 June 2017
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.