Abstract
LetG be a finite primitive linear group over a fieldK, whereK is a finite field or a number field. We bound the composition length ofG in terms of the dimension of the underlying vector space and of the degree ofK over its prime subfield. As a byproduct, we prove a result of number theory which bounds the number of prime factors (counting multiplicities) ofq n−1, whereq, n>1 are integers, improving a result of Turull and Zame [6].
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Languasco, A., Menegazzo, F. & Morigi, M. On the composition length of finite primitive linear groups. Arch. Math 79, 408–417 (2002). https://doi.org/10.1007/BF02638376
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DOI: https://doi.org/10.1007/BF02638376