Translation generalized quadrangles of order (s,s(2)), s even, and eggs

摘要

Characterizations of classical eggs and the classical generalized quadrangle Q(5, s), s even. are given. The egg O(n, 2n, q) = O of PG(4n - 1, q), q even, is classical if and only if either O is good at some element and contains at least one pseudo-conic, or O contains at least two intersecting pseudo-comics. As application three characterizations of the classical generalized quadrangle Q(5, s), s even, are given. (C) 2002 Elsevier Science (USA). [References: 19]