Affine transformations of finite vector spaces with large orders or few cycles

S. Guest; J. Morris; Cheryl Praeger; P. Spiga

doi:10.1016/j.jpaa.2014.04.023

Affine transformations of finite vector spaces with large orders or few cycles

S. Guest, J. Morris, Cheryl Praeger, P. Spiga

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Abstract

© 2014 Elsevier B.V.. Let V be a d-dimensional vector space over a field of prime order p. We classify the affine transformations of V of order at least pd/4, and apply this classification to determine the finite primitive permutation groups of affine type, and of degree n, that contain a permutation of order at least n/4. Using this result we obtain a classification of finite primitive permutation groups of affine type containing a permutation with at most four cycles.

Original language	English
Pages (from-to)	308-330
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	2
DOIs	https://doi.org/10.1016/j.jpaa.2014.04.023
Publication status	Published - Feb 2015

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abstract = "{\textcopyright} 2014 Elsevier B.V.. Let V be a d-dimensional vector space over a field of prime order p. We classify the affine transformations of V of order at least pd/4, and apply this classification to determine the finite primitive permutation groups of affine type, and of degree n, that contain a permutation of order at least n/4. Using this result we obtain a classification of finite primitive permutation groups of affine type containing a permutation with at most four cycles.",

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AB - © 2014 Elsevier B.V.. Let V be a d-dimensional vector space over a field of prime order p. We classify the affine transformations of V of order at least pd/4, and apply this classification to determine the finite primitive permutation groups of affine type, and of degree n, that contain a permutation of order at least n/4. Using this result we obtain a classification of finite primitive permutation groups of affine type containing a permutation with at most four cycles.

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