Premium
An O'Nan‐Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2‐Arc Transitive Graphs
Author(s) -
Praeger Cheryl E.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-47.2.227
Subject(s) - mathematics , combinatorics , transitive relation , permutation graph , cyclic permutation , permutation group , discrete mathematics , bipartite graph , robertson–seymour theorem , arc (geometry) , transitive reduction , graph , permutation (music) , 1 planar graph , line graph , symmetric group , voltage graph , physics , geometry , acoustics
A permutation group is said to be quasiprimitive if each of its nontrivial normal subgroups is transitive. A structure theorem for finite quasiprimitive permutation groups is proved, along the lines of the O'Nan‐Scott Theorem for finite primitive permutation groups. It is shown that every finite, non‐bipartite, 2‐arc transitive graph is a cover of a quasiprimitive 2‐arc transitive graph. The structure theorem for quasiprimitive groups is used to investigate the structure of quasiprimitive 2‐arc transitive graphs, and a new construction is given for a family of such graphs.