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By Eiichi Bannai

ISBN-10: 0805304908

ISBN-13: 9780805304909

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Math. , 2, Janos Bolyai Math. Soc, Budapest (1996), pp. 295-352. [40] V. Lev, Progression-free sets in finite abelian groups, J. Number Theory 104 (2004), 162-169. [41] R. Meshulam, On subsets of finite abelian groups with no 3-term arithmetic progressions, J. Combin. Theory Ser. A 71 (1995), 168-172. [42] G. C. Tao, Restriction and Kakeya phenomena in finite fields, Duke Math. J. 121 (2004), 35-74. [43] B. Nagle, V. Rodl and M. Schacht, The counting lemma for A;-uniform hypergraphs, preprint, 2004.

105-109. [10] J. Bourgain, On triples in arithmetic progression, Geom. Fund. Anal. 9 (1999), 968-984. [11] J. Bourgain, On the dimension of Kakeya sets and related maximal inequalities, Geom. Fund. Anal. 9 (1999), 256-282. -C. Chang, A polynomial bound in Freiman's theorem, Duke Math. J. 113 (2002), 399-419. 24 B. K. L. Graham, Quasi-random subsets of Z n , J. Combin. Theory Ser. A 61 (1992), 64-86. K. L. M. Wilson, Quasi-random graphs, Combinatorica 9 (1989), 345-362. [15] Y. Edel, Extensions of generalized product caps, Designs, Codes and Cryptography 31 (2004), 5-14.

6 ([35]) If G = Spn(q) (with q odd), ft^iq) (with n a multiple of A) or SUn(q), and if Ui is totally isotropic, then H is a maximal subgroup of G, except when G = Spn(q) and (n,q) = (4,3), G = Q+(g) and (n,q) = (4, < 11) or (8,2), and G = SUn(q) and (n,q) = (4,4 or 9). We note that [35] deals with SO^(q) rather than Q+(q), but that the methods are readily adapted for n > 4. In the isomorphism from PQ^(q) to PSL2(q) x PSIi2(q), the copies of PSL2(q) act independently on the two sets of q+\ totally singular lines.

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Algebraic Combinatorics I: Association Schemes (Mathematics lecture note series) (Bk. 1) by Eiichi Bannai

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