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Orbits of Permutation Groups on Unordered Sets, III: Imprimitive Groups
Author(s) -
Cameron Peter J.
Publication year - 1983
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/s2-27.2.229
Subject(s) - permutation group , permutation (music) , mathematics , combinatorics , group (periodic table) , physics , quantum mechanics , acoustics
This paper studies imprimitive groups G having a finite number n k ( G ) of orbits on k ‐sets for all k . The main results are a formula for n k ( G Wr H ) in terms of n k ( G ) and a ‘modified cycle index’ of H , and relations between the growth rate of ( n k ( G )) and the structure of primitive components of G .