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

Original language | English |
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Journal | Proceedings of the Edinburgh Mathematical Society |

DOIs | |

Publication status | E-pub ahead of print - 28 Jun 2019 |

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**Coprime subdegrees of twisted wreath permutation groups.** / Chua, Alexander Y.; Giudici, Michael; Morgan, Luke.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Coprime subdegrees of twisted wreath permutation groups

AU - Chua, Alexander Y.

AU - Giudici, Michael

AU - Morgan, Luke

PY - 2019/6/28

Y1 - 2019/6/28

N2 - 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.

AB - 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.

KW - primitive group

KW - subdegrees

KW - twisted wreath group

UR - http://www.scopus.com/inward/record.url?scp=85068340160&partnerID=8YFLogxK

U2 - 10.1017/S0013091519000130

DO - 10.1017/S0013091519000130

M3 - Article

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

ER -