## Generalized quadrangles and (B,N) pairs |

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1+s+s 1+st Applying lemma automorphism automorphism group axiom B^BrB block containing chain of length Clearly constructed in theorems defined double coset eigenvalues endpoints of chains equations Euclidean plane exists figure fixed points following theorem G is transitive G which fix G1 and G2 given hence i'th row incident point-line pair integer intersection isomorphic length less length n-1 line and t+1 line joining line of Pn lines of G multiplicities noncollinear points nondegenerate nth root number of lines number of points ordinary 3-gon pair G point indexed points and lines points collinear points in S^S points of G points satisfy projective 3-space projective plane proof is complete proper generalized n-gons quadrangle constructed quadrangle with s=t quadric surface root of unity Section set of points shortest chain surface in projective t+1 lines incident Theorem 2.1 theorem is proved three points underlying field Walter Feit Weyl group zero