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Finite Permutation Groups with a Transitive Minimal Normal Subgroup
Author(s) -
Bamberg John,
Praeger Cheryl E.
Publication year - 2004
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/s0024611503014631
Subject(s) - transitive relation , mathematics , permutation group , combinatorics , normal subgroup , permutation (music) , frobenius group , transitive closure , group (periodic table) , discrete mathematics , pure mathematics , chemistry , physics , organic chemistry , acoustics
A finite permutation group is said to be innately transitive if it contains a transitive minimal normal subgroup. In this paper, we give a characterisation and structure theorem for the finite innately transitive groups, as well as describing those innately transitive groups which preserve a product decomposition. The class of innately transitive groups contains all primitive and quasiprimitive groups. 2000 Mathematics Subject Classification 20B05, 20B15.