Hurwitz generation of the universal covering of Alt(n)

TL;DR

This paper proves that the universal covering of most alternating groups Alt(n) retains the Hurwitz property, with only 31 exceptions, most of which can be identified using the genus formula.

Contribution

It establishes that the universal covering of Alt(n) is Hurwitz in almost all cases, identifying specific exceptions and their detectability.

Findings

Universal covering of Alt(n) is Hurwitz for all but 31 cases.

30 exceptions are detectable via the genus formula.

Most exceptions are explicitly characterized.

Abstract

We prove that the universal covering of an alternating group Alt(n) which is Hurwitz is still Hurwitz, with 31 exceptions, 30 of which are detectable by the genus formula.