Permutation representations of the (2, 4, r) triangle groups

Abstract

The abstract triangle groups Δ(2, 4, r) can be defined for any positive integer r by Δ(2, 4, r) = 〈x, y | x2 = y4 = (xy)r = 1〉. In this paper we show that for every r ≥ 6, all but finitely many of the alternating groups An can be obtained as quotients of Δ(2, 4, r).