Fixed point ratios in actions of finite classical groups, I
<p>This is the first in a series of four papers on fixed point ratios in actions of finite classical groups. Our main result states that if <em>G</em> is a finite almost simple classical group and <em>Ω</em> is a faithful transitive non-subspace <em>G</em>-s...
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Формат: | Journal article |
Язык: | English |
Опубликовано: |
Elsevier
2007
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Итог: | <p>This is the first in a series of four papers on fixed point ratios in actions of finite classical groups. Our main result states that if <em>G</em> is a finite almost simple classical group and <em>Ω</em> is a faithful transitive non-subspace <em>G</em>-set then either fpr(<em>x</em>)&lesssim;|<em>x</em><sup><em>G</em></sup>|<sup>−1/2</sup> for all elements <em>x</em>∈<em>G</em> of prime order, or (<em>G, Ω</em>) is one of a small number of known exceptions. Here fpr(<em>x</em>) denotes the proportion of points in <em>Ω</em> which are fixed by <em>x</em>. In this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups. A further application concerning monodromy groups of covers of Riemann surfaces is also outlined.</p> |
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