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Bounding the composition length of primitive permutation groups and completely reducible linear groups
Author(s) -
Glasby S. P.,
Praeger Cheryl E.,
Rosa Kyle,
Verret Gabriel
Publication year - 2018
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.12138
Subject(s) - bounding overwatch , mathematics , upper and lower bounds , composition (language) , permutation group , combinatorics , permutation (music) , group (periodic table) , degree (music) , primitive permutation group , symmetric group , cyclic permutation , mathematical analysis , computer science , physics , linguistics , philosophy , quantum mechanics , artificial intelligence , acoustics
We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds on the composition length of a finite completely reducible linear group in terms of some of its parameters. In almost all cases we show that the bounds are sharp, and describe the extremal examples.