Abstract
In a previous paper the authors with M. Conder proved that the alternating group An and the symmetric group Sn are pseudo-Hurwitz for any n>23, as well as are A18, A19, A21, A22 and A23, and also S10, S17, S19, S20, S21 and S22. In this paper, we provide geometric tools for constructing all pseudo-Hurwitz groups up to a “small” degree. This construction, applied up to degree 23, shows that there are no other degrees for which An and Sn are pseudo-Hurwitz.In the second part of this paper we show that there are both reflexible and chiral pseudo-Hurwitz maps with automorphism group An and Sn, for every n⩾36.
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