on 32-Transitive Frobenius Regular Groups

Camina, A. R.; McDermott, John P. J.

doi:10.1112/jlms/s2-20.2.205

Cited by 6 publications

(2 citation statements)

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“…(iii) n = 1 2 q(q − 1) where q = 2 f 8, and either G = PSL 2 (q) or G = PΓL 2 (q) with f prime; the size of the nontrivial subdegrees is q + 1 or f (q + 1), respectively. [53], and Camina and McDermott [17]. A characterisation of the groups in (i) and (iii) as the only 3 2 -transitive groups with trivial Fitting subgroup and all two-point stabilisers conjugate was given by Zieschang [69].…”

Section: Introductionmentioning

confidence: 99%

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The classification of almost simple $\tfrac {3}{2}$-transitive groups

Bamberg

Giudici

Liebeck

et al. 2013

Trans. Amer. Math. Soc.

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A finite transitive permutation group is said to be 3 2 -transitive if all the nontrivial orbits of a point stabiliser have the same size greater than 1. Examples include the 2-transitive groups, Frobenius groups and several other less obvious ones. We prove that 3 2 -transitive groups are either affine or almost simple, and classify the latter. One of the main steps in the proof is an arithmetic result on the subdegrees of groups of Lie type in characteristic p: with some explicitly listed exceptions, every primitive action of such a group is either 2-transitive, or has a subdegree divisible by p.

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Section: Introductionmentioning

confidence: 99%

“…, SO + 4 (3).2 SL 4 (3). It is not difficult to find the subdegrees directly by computer for , 24 2 , 32, 36 3 , 48 2 , 72 5 , 1449 , 192, 28817 , 5766 …”

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confidence: 99%