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On a theorem of Wielandt concerning simply primitive groups

Published online by Cambridge University Press:  24 October 2008

G. A. Jones  and
K. D. Soomro
G. A. Jones
Affiliation:
University of Southampton, Pakistan
K. D. Soomro
Affiliation:
University of SindPakistan
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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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References

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