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ON SUBGROUPS OF PRIME POWER INDEX

Published online by Cambridge University Press:  08 January 2001

BARBARA BAUMEISTER
BARBARA BAUMEISTER
Affiliation:
Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ
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Abstract

All finite groups G are determined that admit a subgroup K of index pa, p a prime, under the assumption that G has an irreducible and faithful GF(q)-module in characteristic p whose dimension over GF(q) is at most a. As an application to the theory of permutation groups, the maximal transitive subgroups of the primitive affine permutation groups are determined. The above-mentioned classification is generalized by dropping the assumption that p|q. In both cases surprisingly nice results are obtained.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 407 - 422
Copyright
The London Mathematical Society 2000

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