Coprime subdegrees of twisted wreath permutation groups

Alexander Y. Chua, Michael Giudici, Luke Morgan

Research output: Contribution to journalArticlepeer-review


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, we obtain a full classification of all pairs of non-trivial coprime subdegrees.

Original languageEnglish
Pages (from-to)1137-1162
Number of pages26
JournalProceedings of the Edinburgh Mathematical Society
Issue number4
Early online date28 Jun 2019
Publication statusPublished - 1 Nov 2019


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