Coprime subdegrees of twisted wreath permutation groups. Issue 4 (28th June 2019) - Chua, Alexander Y.; Giudici, Michael; Morgan, Luke
Abstract: Dolfi, Guralnick, Praeger and Spiga asked whether there exist infinitely many primitive groups of twisted wreath type with non-trivial coprime subdegrees. Here, we settle this question in the affirmative. We construct infinite families of primitive twisted wreath permutation groups with non-trivial coprime subdegrees. In particular, we define a primitive twisted wreath group G ( m, q ) constructed from the non-abelian simple group PSL(2, q ) and a primitive permutation group of diagonal type with socle PSL(2, q ) m, and determine many subdegrees for this group. A consequence is that we determine all values of m and q for which G ( m, q ) has non-trivial coprime subdegrees. In the case where m = 2 and q otin {7, 11, 29}, we obtain a full classification of all pairs of non-trivial coprime subdegrees.