A note on the product of two permutations of prescribed orders. (October 2016) - König, J.
Abstract: We prove a conjecture by Stefan Kohl on the existence of triples of permutations of bounded degree with prescribed orders and product 1 . More precisely, let a, b, c be integers, all ≥ 2 . Then there exist elements x, y, z ∈ S c + 2 of orders a, b and c respectively, with x y z = 1 . This result leads to an existence result for covers of the complex projective line with bounded degree and prescribed ramification indices.