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.

中文翻译：

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扭曲花环排列群的互质次度

Dolfi、Guralnick、Praeger 和 Spiga 询问是否存在无限多个具有非平凡互质次度的扭曲花环类型的原始群。在这里，我们肯定地解决这个问题。我们构建了具有非平凡互质子度的原始扭曲花环置换群的无限族。特别是，我们定义了一个原始的扭曲花环组G(米,q) 由非阿贝尔单群 PSL(2,q) 和具有 socle PSL(2,q)米，并确定该组的许多子度数。结果是我们确定了所有的值米和q为此G(米,q) 具有非平凡的互质次度。在这种情况下米= 2 和$q\notin \{7,11,29\}$，我们获得了所有非平凡互质子度对的完整分类。