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Abstract
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The sets of primitive, quasiprimitive, and innately transitive permutation groups may
each be regarded as the building blocks of finite transitive permutation groups, and
are analogues of composition factors for abstract finite groups. This paper extends
classifications of finite primitive and quasiprimitive groups of rank at most
to a
classification for the finite innately transitive groups. The new examples comprise
three infinite families and three sporadic examples. A necessary step in this
classification was the determination of certain configurations in finite almost simple
-transitive
groups called special pairs.
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Dedicated to the memory of Jacques
Tits
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Keywords
rank 3, permutation group, partial linear space, innately
transitive, 2-transitive
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Mathematical Subject Classification
Primary: 20B05, 20B10, 20B20
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Milestones
Received: 22 August 2022
Revised: 5 November 2022
Accepted: 4 December 2022
Published: 13 September 2023
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© 2023 MSP (Mathematical Sciences
Publishers). |
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