Coprime Subdegrees of Twisted Wreath Permutation Groups
Abstract
Dolfi, Guralnick, Praeger and Spiga asked if there exist infinitely many primitive groups of twisted wreath type with nontrivial coprime subdegrees. Here we settle this question in the affirmative. We construct infinite families of primitive twisted wreath permutation groups with nontrivial coprime subdegrees. In particular, we define a primitive twisted wreath group $G(m,q)$ constructed from the nonabelian simple group $\text{PSL}(2,q)$ and a primitive permutation group of diagonal type with socle $\text{PSL}(2,q)^m$, and determine all values of $m$ and $q$ for which $G(m,q)$ has nontrivial coprime subdegrees. In the case where $m=2$ and $q\notin\{7,11,29\}$ we obtain a full classification of all pairs of nontrivial coprime subdegrees.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 DOI:
 10.48550/arXiv.1801.02456
 arXiv:
 arXiv:1801.02456
 Bibcode:
 2018arXiv180102456C
 Keywords:

 Mathematics  Group Theory;
 20B15
 EPrint:
 Proceedings of the Edinburgh Mathematical Society 62 (2019) 11371162