Coprime subdegrees of twisted wreath permutation groups. Issue 4 (28th June 2019)

• Record Type: Journal Article
• Authors: Chua, Alexander Y.; Giudici, Michael; Morgan, Luke
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 62:Issue 4(2019)
• Page Start: 1137
• Page End: 1162
• Publication Date: 2019-06-28
• Subjects: primitive group, -- twisted wreath group, -- subdegrees; Primary 20B15, -- 20H30, -- 20B05; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091519000130
• Languages: English
• ISSNs: 0013-0915

Abstract

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 $q\notin \{7, 11, 29\}$, we obtain a full classification of all pairs of non-trivial coprime subdegrees.