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On imprimitive rank 3 permutation groups
Author(s) -
Devillers Alice,
Giudici Michael,
Li Cai Heng,
Pearce Geoffrey,
Praeger Cheryl E.
Publication year - 2012
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/jdr074
Subject(s) - alice (programming language) , rank (graph theory) , citation , permutation (music) , computer science , library science , combinatorics , classics , mathematics , history , philosophy , programming language , aesthetics
A classification is given of rank 3 group actions which are quasiprimitivebut not primitive. There are two infinite families and a finite number ofindividual imprimitive examples. When combined with earlier work of Bannai,Kantor, Liebler, Liebeck and Saxl, this yields a classification of allquasiprimitive rank 3 permutation groups. Our classification is achieved byfirst classifying imprimitive almost simple permutation groups which induce a2-transitive action on a block system and for which a block stabiliser acts2-transitively on the block. We also determine those imprimitive rank 3permutation groups $G$ such that the induced action on a block is almost simpleand $G$ does not contain the full socle of the natural wreath product in which$G$ embeds.Comment: updated after revision