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On the orders of primitive linear P'-groups

Published online by Cambridge University Press:  17 April 2009

A. Gambini Weigel  and
T.S. Weigel
A. Gambini Weigel
Affiliation:
Mathematishces Institut Albert-Ludwigs-Universität, Albertstr.23b D78 Freiburg
T.S. Weigel
Affiliation:
Mathematishces Institut Albert-Ludwigs-Universität, Albertstr.23b D78 Freiburg
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A group G ≤ GLK(V) is called K-primitive if there exists no non-trivial decomposition of V into a sum of K-spaces which is stabilised by G. We show that if V is a finite vector space and G a K-primitive subgroup of GLK(V) whose order is coprime to |V|, we can bound the order of G by |V|log2(|V|) apart from one exception. Later we use this result to obtain some lower bounds on the number of p–singular elements in terms of the group order and the minimal representation degree.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 3 , December 1993 , pp. 495 - 521
Copyright
Copyright © Australian Mathematical Society 1993

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