On Beauville structures on the groups S_n and A_n

摘要

It is known that the symmetric group S_n, for n ≥ 5, and the alternating group A_n, for large n, admit a Beauville structure. In this paper we prove that A_n admits a Beauville (resp. strongly real Beauville) structure if and only if n ≥ 6 (resp n ≥ 7). We also show that S_n admits a strongly real Beauville structure for n ≥ 5.