Minimal set of generators of symplectic groups over finite fields
نویسندگان
چکیده
منابع مشابه
Generators and irreducible polynomials over finite fields
Weil’s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field. An application to the distribution of irreducible polynomials is given, which confirms an asymptotic version of a conjecture of Hansen-Mullen.
متن کاملHeisenberg groups over finite fields
ing this computation, for given k-vectorspace V with non-degenerate alternating form 〈, 〉, put a Lie algebra [2] structure h on V ⊕ k by Lie bracket [v ⊕ z, v′ ⊕ z′] = 0⊕ 〈v, v′〉 In exponential coordinates on H, the exponential map h→ H with H ≈ V ⊕ k is notated exp(v ⊕ z) = v ⊕ z with Lie group structure on H by (v ⊕ z) · (v′ ⊕ z′) = (v + v′)⊕ (z + z′ + 〈v, v ′〉 2 ) (exponential coordinates in...
متن کاملA Characterization of the Unitary and Symplectic Groups over Finite Fields of Characteristic at Least 5
A much larger class of groups satisfies the analogous property for p — 2 or 3, including many of the sporatic simple groups. The classification for p = 2 appears in [3]. The classification for p = 3 is incomplete, but a partial solution appears in [4] For the most part the proof here mimics that in the papers mentioned above. The exception comes in handling certain degenerate cases. This is acc...
متن کاملCharacters of unipotent groups over finite fields
Let G be a connected unipotent group over a finite field Fq. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(Fq) and give an explicit description of L-packets in terms of the so-called “admissible pairs” for G. We then apply our results to show that if the centralizer of every geometric point of G is connected, then the dimension...
متن کاملCharacters of Reductive Groups over Finite Fields
Let E be a connected reductive algebraic group over C and let W be its Weyl group. The Springer correspondence allows us to parametrize the irreducible representations E of W as F = F^^ where u is a unipotent element in G (up to conjugacy) and <p is an irreducible representation of the group of components AH(u) = ZH(u)IZ°H(u). (However, not all <p arise in the parametrization.) For F = F^Uttp) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1980
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1980.101710