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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| Format: | Journal article |
| Language: | English |
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Elsevier
2007
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| _version_ | 1826260805850497024 |
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| author | Burness, T |
| author_facet | Burness, T |
| author_sort | Burness, T |
| collection | OXFORD |
| description | <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> |
| first_indexed | 2024-03-06T19:11:34Z |
| format | Journal article |
| id | oxford-uuid:16f3af02-143c-46a3-a61c-49a9f0dea93f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:11:34Z |
| publishDate | 2007 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:16f3af02-143c-46a3-a61c-49a9f0dea93f2022-03-26T10:34:18ZFixed point ratios in actions of finite classical groups, IJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:16f3af02-143c-46a3-a61c-49a9f0dea93fMathematicsGroup theory and generalizations (mathematics)EnglishOxford University Research Archive - ValetElsevier2007Burness, T<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> |
| spellingShingle | Mathematics Group theory and generalizations (mathematics) Burness, T Fixed point ratios in actions of finite classical groups, I |
| title | Fixed point ratios in actions of finite classical groups, I |
| title_full | Fixed point ratios in actions of finite classical groups, I |
| title_fullStr | Fixed point ratios in actions of finite classical groups, I |
| title_full_unstemmed | Fixed point ratios in actions of finite classical groups, I |
| title_short | Fixed point ratios in actions of finite classical groups, I |
| title_sort | fixed point ratios in actions of finite classical groups i |
| topic | Mathematics Group theory and generalizations (mathematics) |
| work_keys_str_mv | AT burnesst fixedpointratiosinactionsoffiniteclassicalgroupsi |