The Primitive Soluble Permutation Groups of Degree Less Than 256, Volume 1519This monograph addresses the problem of describing all primitive soluble permutation groups of a given degree, with particular reference to those degrees less than 256. The theory is presented in detail and in a new way using modern terminology. A description is obtained for the primitive soluble permutation groups of prime-squared degree and a partial description obtained for prime-cubed degree. These descriptions are easily converted to algorithms for enumerating appropriate representatives of the groups. The descriptions for degrees 34 (die vier hochgestellt, Sonderzeichen) and 26 (die sechs hochgestellt, Sonderzeichen) are obtained partly by theory and partly by machine, using the software system Cayley. The material is appropriate for people interested in soluble groups who also have some familiarity with the basic techniques of representation theory. This work complements the substantial work already done on insoluble primitive permutation groups. |
Contents
Introduction | 1 |
Conclusion | 10 |
The imprimitive soluble subgroups of GL2pk | 43 |
Copyright | |
9 other sections not shown
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The Primitive Soluble Permutation Groups of Degree Less than 256 Mark W. Short No preview available - 1992 |
Common terms and phrases
abelian normal subgroup absolutely irreducible algorithm automorphism Burnside inclusion diagram C₂ CAYLEY Chapter characteristic subgroup complete and irredundant completely reducible conjugacy class conjugacy class representatives contains cyclic group denote determine diagonal elements of order F has type finite field Fitting subgroup follows G₁ G₂ GL(q group isomorphic groups of degree groups of order imprimitive soluble subgroups irreducible soluble subgroups irreducible subgroups irredundant list irredundant set isomorphism type ISOTEST isotropic subspace JS-imprimitive JS-maximals JS-primitive lattice Lemma Let G linear groups M₁ M₂ matrix maximal abelian normal maximal soluble subgroups natural module non-abelian normaliser polycyclic presentation prime primitive groups primitive maximal soluble primitive permutation groups primitive subgroups Proof q is odd scalar group Singer cycle soluble permutation groups subgroup of G subgroup of order subgroups of GL(n Suprunenko 1976 Sylow 2-subgroups symplectic group system of imprimitivity Theorem theory unique maximal abelian V₁ wreath product X₁