A note on the product of two permutations of prescribed orders. (October 2016)

• Record Type: Journal Article
• Authors: König, J.
• Is Part Of: European journal of combinatorics. Volume 57(2016:Oct.)
• Page Start: 50
• Page End: 56
• Publication Date: 2016-10
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.03.006
• Languages: English
• ISSNs: 0195-6698

Abstract

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.