Abstract
We improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.
Original language | English |
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Pages (from-to) | 201-204 |
Number of pages | 4 |
Journal | Archiv der Mathematik |
Volume | 105 |
Issue number | 3 |
Early online date | 21 Aug 2015 |
DOIs | |
Publication status | Published - Sept 2015 |
Keywords
- Symmetric group
- Alternating group
- Generation
- Probability