Coprime subdegrees of twisted wreath permutation groups

Author:

Chua Alexander Y.,Giudici Michael,Morgan Luke

Abstract

AbstractDolfi, 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference15 articles.

1. The Inclusion Problem for Finite Primitive Permutation Groups

2. On minimal subdegrees of finite primitive permutation groups;Giudici;Finite geometries, groups, and computation,2006

3. J. Fawcett , Bases of primitive permutation groups. PhD thesis, University of Cambridge, 2013.

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