A group G less-than-or-equal-to GL(K)(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 GL(K)(V) whose order is coprime to Absolute value of V, we can bound the order of G by Absolute value of 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
Weigel, A., Weigel, T. (1993). On the orders of primitive linear P'-groups. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 48(3), 495-521 [10.1017/S0004972700015951].
On the orders of primitive linear P'-groups
WEIGEL, THOMAS STEFAN
1993
Abstract
A group G less-than-or-equal-to GL(K)(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 GL(K)(V) whose order is coprime to Absolute value of V, we can bound the order of G by Absolute value of 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
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