On the orders of primitive groups with restricted nonabelian composition factors

L. Babai; P. J. Cameron; P. P. Pálfy

doi:10.1016/0021-8693(82)90323-4

On the orders of primitive groups with restricted nonabelian composition factors

L. Babai^*, P. J. Cameron, P. P. Pálfy

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that, given c₀, there exists c such that the following holds. If G is a primitive permutation group of degree n, no composition factor of which is an alternating group of degree greater than c₀ or a classical group of dimension greater than c₀, then |G|≤n^c. In particular, if the nonabelian composition factors of G have bounded order, then |G| is polynomially bounded.

Original language	English
Pages (from-to)	161-168
Number of pages	8
Journal	Journal of Algebra
Volume	79
Issue number	1
DOIs	https://doi.org/10.1016/0021-8693(82)90323-4
Publication status	Published - 1 Jan 1982

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abstract = "We prove that, given c0, there exists c such that the following holds. If G is a primitive permutation group of degree n, no composition factor of which is an alternating group of degree greater than c0 or a classical group of dimension greater than c0, then |G|≤nc. In particular, if the nonabelian composition factors of G have bounded order, then |G| is polynomially bounded.",

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N2 - We prove that, given c0, there exists c such that the following holds. If G is a primitive permutation group of degree n, no composition factor of which is an alternating group of degree greater than c0 or a classical group of dimension greater than c0, then |G|≤nc. In particular, if the nonabelian composition factors of G have bounded order, then |G| is polynomially bounded.

AB - We prove that, given c0, there exists c such that the following holds. If G is a primitive permutation group of degree n, no composition factor of which is an alternating group of degree greater than c0 or a classical group of dimension greater than c0, then |G|≤nc. In particular, if the nonabelian composition factors of G have bounded order, then |G| is polynomially bounded.

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On the orders of primitive groups with restricted nonabelian composition factors

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