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A note on extremely primitive affine groups
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Burness, Timothy C. and Thomas, Adam (2021) A note on extremely primitive affine groups. Archiv der Mathematik, 116 . pp. 141-152. doi:10.1007/s00013-020-01528-2 ISSN 0003-889X.
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Official URL: https://doi.org/10.1007/s00013-020-01528-2
Abstract
Let G be a nite primitive permutation group on a set with nontrivial point stabilizer G . We say that G is extremely primitive if G acts primitively on each of its orbits in n f g. In earlier work, Mann, Praeger and Seress have proved that every extremely primitive group is either almost simple or of a ne type and they have classi ed the a ne groups up to the possibility of at most nitely many exceptions. More recently, the almost simple extremely primitive groups have been completely determined. If one assumes Wall's conjecture on the number of maximal subgroups of almost simple groups, then the results of Mann et al. show that it just remains to eliminate an explicit list of a ne groups in order to complete the classi cation of the extremely primitive groups. Mann et al. have conjectured that none of these a ne candidates are extremely primitive and our main result con rms this conjecture.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Maximal subgroups, Finite groups, Group theory, Representations of groups, Linear algebraic groups, Geometry, Algebraic | ||||||||
Journal or Publication Title: | Archiv der Mathematik | ||||||||
Publisher: | Birkhaeuser Verlag AG | ||||||||
ISSN: | 0003-889X | ||||||||
Official Date: | February 2021 | ||||||||
Dates: |
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Volume: | 116 | ||||||||
Page Range: | pp. 141-152 | ||||||||
DOI: | 10.1007/s00013-020-01528-2 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 10 September 2020 | ||||||||
Date of first compliant Open Access: | 2 November 2020 | ||||||||
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