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Closures of Finite Primitive Permutation Groups
Author(s) -
Praeger Cheryl E.,
Saxl Jan
Publication year - 1992
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/24.3.251
Subject(s) - mathematics , primitive permutation group , combinatorics , permutation group , permutation (music) , invariant (physics) , closure (psychology) , cyclic permutation , symmetric group , mathematical physics , physics , acoustics , economics , market economy
Let G be a primitive permutation group on a finite set Ω, and, for k ⩾ 2, let G ( k ) be the k ‐closure of G , that is, the largest subgroup of Sym (Ω) preserving all the G ‐invariant k ‐relations on Ω. Suppose that G < H ⩽ G ( k ) and G and H have different socles. It is shown that k ⩽5 and the groups G and H are classified explicitly.