Arc-transitive digraphs with quasiprimitive local actions

Giudici, Michael1; Glasby, S. P.1; Li, Cai Heng2; Verret, Gabriel1,3,4

2019-03

10.1016/j.jpaa.2018.06.002

JOURNAL OF PURE AND APPLIED ALGEBRA   影响因子和分区

0022-4049

1873-1376

Let Gamma be a finite G-vertex-transitive digraph. The in-local action of (Gamma, G) is the permutation group L- induced by a vertex-stabiliser on the set of in-neighbours of the corresponding vertex. The out-local action L+ is defined analogously. Note that L- and L+ may not be isomorphic. We thus consider the problem of determining which pairs (L-, L+) are possible. We prove some general results, but pay special attention to the case when L- and L+ are both quasiprimitive. (Recall that a permutation group is quasiprimitive if each of its nontrivial normal subgroups is transitive.) Along the way, we prove a structural result about pairs of finite quasiprimitive groups of the same degree, one being (abstractly) isomorphic to a proper quotient of the other. (C) 2018 Elsevier B.V. All rights reserved.

SCI

英语

其他

NSFC[11771200]

Mathematics

Mathematics, Applied ; Mathematics

WOS:000449246900020

ELSEVIER SCIENCE BV

MATHEMATICS

Web of Science

1.Univ Western Australia, Ctr Math Symmetry & Computat, 35 Stirling Highway, Crawley, WA 6009, Australia
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
3.Univ Primorska, FAMNIT, Glagoljaska 8, SI-6000 Koper, Slovenia
4.Univ Auckland, Dept Math, Private Bag 92019, Auckland 1142, New Zealand

Giudici, Michael,Glasby, S. P.,Li, Cai Heng,et al. Arc-transitive digraphs with quasiprimitive local actions[J]. JOURNAL OF PURE AND APPLIED ALGEBRA,2019,223(3):1217-1226.

Giudici, Michael,Glasby, S. P.,Li, Cai Heng,&Verret, Gabriel.(2019).Arc-transitive digraphs with quasiprimitive local actions.JOURNAL OF PURE AND APPLIED ALGEBRA,223(3),1217-1226.

Giudici, Michael,et al."Arc-transitive digraphs with quasiprimitive local actions".JOURNAL OF PURE AND APPLIED ALGEBRA 223.3(2019):1217-1226.