منابع مشابه
Linear Groups Containing a Singer Cycle*
I f G induces a primitive permutation group on the set X of points (l-spaces) of the underlying vector space V, then well-known results of Burnside [I, p. 3411 and Schur [6] imply that G acts on X 2-transitively or as a regular or Frobenius group of prime degree; the theorem then follows from [2; 51. We must thus take a nontrivial block of imprimitivity d for G on X, and analyze the action of G...
متن کاملNilpotent Singer Groups
Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order a...
متن کاملOptical Orthogonal Codes from Singer Groups
We construct some new families of optical orthogonal codes that are asymptotically optimal. In particular, for any prescribed value of λ, we construct infinite families of (n, w, λ)-OOCs that in each case are asymptotically optimal. Our constructions rely on various techniques in finite projective spaces involving normal rational curves and Singer groups. These constructions generalize and impr...
متن کاملOn the three-dimensional Singer Conjecture for Coxeter groups
We give a proof of the Singer conjecture (on the vanishing of reduced l-homology except in the middle dimension) for the Davis Complex Σ associated to a Coxeter system (W,S) whose nerve L is a triangulation of S . We show that it follows from a theorem of Andreev, which gives the necessary and sufficient conditions for a classical reflection group to act on H.
متن کامل2-dimensional Optical Orthogonal Codes from Singer Groups
We present several new families of (Λ × T,w, λ) (2-D) wavelength/time optical orthogonal codes (2D-OOCs) with λ = 1, 2. All families presented are either optimal with respect to the Johnson bound (J-optimal) or are asymptotically optimal. The codes presented have more flexible dimensions and weight than the J-optimal families appearing in the literature. The constructions are based on certain p...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90214-8