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The finite primitive groups with soluble stabilizers, and the edge‐primitive s ‐arc transitive graphs
Author(s) -
Li Cai Heng,
Zhang Hua
Publication year - 2011
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdr004
Subject(s) - mathematics , combinatorics , primitive permutation group , permutation group , transitive relation , simple (philosophy) , permutation graph , affine transformation , classification of finite simple groups , discrete mathematics , permutation (music) , graph , symmetric group , cyclic permutation , group of lie type , pure mathematics , group theory , philosophy , physics , epistemology , acoustics
Motivated by the study of several problems in algebraic graph theory, we study finite primitive permutation groups whose point stabilizers are soluble. Such primitive permutation groups are divided into three types: affine, almost simple and product action, and the product action type can be reduced to the almost simple type. This paper gives an explicit list of the soluble maximal subgroups of almost simple groups. The classification is then applied to classify edge‐primitive s ‐arc transitive graphs with s ⩾ 4, solving a problem proposed by Richard M. Weiss (1999).