Orthogonal starters in finite abelian groups
نویسندگان
چکیده
منابع مشابه
Designing Local Orthogonal Bases on Finite Groups I: Abelian Case
(a) (b) (c) b b ˆ Figure 1: Geometric interpretation of the orthogonalization procedure using the Fourier transform as a tool. The group is ? = fI; V g, where V performs the exchange of the components of vectors from R 2. (a) Projection of b on the ?-invariant subspaces relative to U 1 and U ?1. (b) Normalization of the two projections. (c) Recombination of the normalized projections yielding t...
متن کاملDecomposing finite Abelian groups
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to be at least as difficult as factoring).
متن کاملFactoring finite abelian groups
It is shown that if in the factorization of a finite cyclic group each factor has either prime power order or order equal to the product of two primes then one factor must be periodic. This is shown to be the best possible result of this type. 2004 Elsevier Inc. All rights reserved.
متن کاملOn non-normal non-abelian subgroups of finite groups
In this paper we prove that a finite group $G$ having at most three conjugacy classes of non-normal non-abelian proper subgroups is always solvable except for $Gcong{rm{A_5}}$, which extends Theorem 3.3 in [Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable, Acta Math. Sinica (English Series) 27 (2011) 891--896.]. Moreover, we s...
متن کاملFinite $p$-groups and centralizers of non-cyclic abelian subgroups
A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
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: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90335-f