منابع مشابه
p-RANKS AND AUTOMORPHISM GROUPS OF ALGEBRAIC CURVES
Let X be an irreducible complete nonsingular curve of genus g over an algebraically closed field k of positive characteristic p. If g > 2, the automorphism group Aut(X) of X is known to be a finite group, and moreover its order is bounded from above by a polynomial in g of degree four (Stichtenoth). In this paper we consider the p-rank -7 of X and investigate relations between if and Aut(X). We...
متن کاملOn the Ranks of Finite Simple Groups
Let G be a finite group and let X be a conjugacy class of G. The rank of X in G, denoted by rank(G:X) is defined to be the minimal number of elements of X generating G. In this paper we review the basic results on generation of finite simple groups and we survey the recent developments on computing the ranks of finite simple groups.
متن کاملSOME SIMPLE MODULES FOR CLASSICAL GROUPS AND p-RANKS OF ORTHOGONAL AND HERMITIAN GEOMETRIES
We determine the characters of the simple composition factors and the submodule lattices of certain Weyl modules for classical groups. The results have several applications. The simple modules arise in the study of incidence systems in finite geometries and knowledge of their dimensions yields the p-ranks of these incidence systems.
متن کاملSome p-Ranks Related to Orthogonal Spaces*
We determine the p-rank of the incidence matrix of hyperplanes of PG(n, pe) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in O10(2e), O10(3e), O9(5e), O12(5e) and O12(7e). We also give slightly weaker bounds for more general finite classical polar spaces. Another applic...
متن کاملSome p-ranks Related to Hermitian Varieties
We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p) and points of a nondegenerate Hermitian variety. As a corollary, we obtain new bounds for the size of caps and the existence of ovoids in finite unitary spaces. This paper is a companion to [2], in which Blokhuis and this author derive the analogous p-ranks for quadrics.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11245-6