Theory of Association Schemes / by Paul-Hermann Zieschang.

Springer eBooks

Basic Facts -- Basic Technics -- Quotient Schemes -- Morphisms -- Normal Closed Subsets -- Products -- Thin Schemes -- Scheme Algebras -- Dihedral Closed Subsets -- Constrained Sets of Involutions -- The Exchange Condition -- Spherical Coxeter Schemes -- Historical Notes.

Theory of Association Schemes is the first concept-oriented treatment of the structure theory of association schemes. It contains several recent results which appear for the first time in book form. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type. Also a scheme-theoretic characterization of Glauberman’s Z*-involutions is included. The text is self-contained and accessible for advanced undergraduate students.

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