On a theorem of Wielandt concerning simply primitive groups
Published online by Cambridge University Press: 24 October 2008
Extract
Let G be a simply primitive permutation group on a set Ω of order p2, where p is a prime (necessarily odd). In theorem 27·2 of (9), Wielandt states without proof:
Theorem A. (i) ¦G¦ is not divisible by p3;
(ii) if G has a pair of Sylow p-subgroups with nontrivial intersection, then G has an imprimitive subgroup of index 2 which is the direct product of two intransitive groups.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 3 , November 1982 , pp. 419 - 423
- Copyright
- Copyright © Cambridge Philosophical Society 1982
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