TY - JOUR
T1 - Permutation groups and derangements of odd prime order
AU - Burness, Timothy C.
AU - Giudici, Michael
PY - 2017/10/1
Y1 - 2017/10/1
N2 - Let G be a transitive permutation group of degree n. We say that G is 2′-elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 2′-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate automorphisms of finite arc-transitive graphs of prime valency.
AB - Let G be a transitive permutation group of degree n. We say that G is 2′-elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 2′-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate automorphisms of finite arc-transitive graphs of prime valency.
KW - Arc-transitive graph
KW - Biquasiprimitive group
KW - Derangement
KW - Elusive group
KW - Quasiprimitive group
UR - http://www.scopus.com/inward/record.url?scp=85018247728&partnerID=8YFLogxK
UR - https://arxiv.org/abs/1602.07617
U2 - 10.1016/j.jcta.2017.04.007
DO - 10.1016/j.jcta.2017.04.007
M3 - Article
AN - SCOPUS:85018247728
VL - 151
SP - 102
EP - 130
JO - Journal of Combinatorial Theory Series A
JF - Journal of Combinatorial Theory Series A
SN - 0021-9800
ER -