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On Subgroups of Prime Power Index
Author(s) -
Baumeister Barbara
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001125
Subject(s) - mathematics , prime (order theory) , combinatorics , permutation (music) , prime power , transitive relation , affine transformation , permutation group , dimension (graph theory) , normal subgroup , primitive permutation group , index (typography) , discrete mathematics , group (periodic table) , symmetric group , pure mathematics , cyclic permutation , physics , computer science , world wide web , acoustics , quantum mechanics
All finite groups G are determined that admit a subgroup K of index p a , 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.