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Originally published in 1946 as number thirty-nine in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding linear groups. Appendices are also included. This book will be of value to anyone with an interest in linear groups and the history of mathematics.
Table des matières
Preface; Introduction; 1. The fundamental notation; 2. The equation of the Burkhardt primal; 3. Similarity, or equal standing, of the forty-five nodes, and of the twenty-seven pentahedra; 4. The Jacobian planes of the primal; 5. The k-lines of the primal; 6. The Burkhardt primal is rational; 7. The particular character of the forty-five nodes, and the linear transformation of the primal into itself by projection from the nodes; 8. The forty Steiner threefold spaces, or primes, belonging to the primal; 9. The plane common to two Steiner solids; 10. The enumeration of the twenty-seven Jordan pentahedra, and of the forty-five nodes, from the nodes in pairs of polar k-lines; 11. The reason for calling the Steiner tetrahedra by this name; 12. The enumeration of the twenty-seven pentahedra from nine nodes of the Burkhardt primal; 13. The equation of the Burkhardt primal in terms of a Steiner solid and four association primes; 14. Explicit formulae for the rationalization of the Burkhardt primal; 15. The equation of the Burkhardt primal referred to the prime faces of a Jordan pentahedron; 16. The thirty-six double sixes of Jordan pentahedra, and the associated quadrics; 17. The linear transformations of the Burkhardt primal into itself; 18. Five subgroups of the group 23.34.40 transformations; 19. The expression of the fundamental transformations B, C, D, S as transformations of x1,...,x6. The expression of B, C, D, S in terms of nodal projections; 20. The application of the substitutions of x1,...,x6 to the twelve pentahedra {A}, {B},..., {F0}; 21. The transformation of the family {A} by means of Burkhardt's transformations; 22. Derivation of the Burkhardt primal from a quadratic; Appendix, note 1. The generation of desmic systems of tetrahedra in ordinary space; Appendix, note 2. On the group of substitutions of the lines of a cubic surface in ordinary space; Index of notations.
Résumé
Originally published in 1946 as number thirty-nine in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding linear groups. Appendices are also included. This book will be of value to anyone with an interest in linear groups and the history of mathematics.
