منابع مشابه
Primitive Elements
Importantly, there is no element 1 ≤ k < p − 1 such that a ≡ 1(modp). The concepts presented in the study of primitive elements can be considered special cases of more general idea presented in group theory. Specifically, the primitve element a can be seen as a generator of Zp, we wil discuss this in more detail in the first section of the paper. Primitive elements also have applications in enc...
متن کاملFinite Field Elements with Specified Order and Traces
Results of F. Özbudak on the existence of elements in a finite extension of a finite field with specified order and at which given rational functions have specified traces over the ground field are obtained by the method of character sums. There are significant applications to the construction of ordered arrays.
متن کاملPrimitive Zero-Symmetric Sign Pattern Matrices with Zero Diagonal Attaining the Maximum Base
A sign pattern matrix or sign pattern A is a matrix whose entries are from the set {1,−1, 0}. Notice that for a square sign pattern matrixA, in the computation of the signs of the entries of the power A, an ambiguous sign may arise when a positive sign is added to a negative sign. So a new symbol # was introduced in 1 to denote such an ambiguous sign. The powers of a square sign pattern have be...
متن کاملAn Algebra of Skew Primitive Elements
We study the various term operations on the set of skew primitive elements of Hopf algebras, generated by skew primitive semi-invariants of an Abelian group of grouplike elements. All 1-linear binary operations are described and trilinear and quadrilinear operations are given a detailed treatment. Necessary and sufficient conditions for the existence of multilinear operations are specified in t...
متن کاملCounting Primitive Elements in Free Groups
In this paper it is proved that the set of primitive elements of a nonabelian free group has density zero, i.e. the ratio of primitive elements in increasingly large balls is arbitrarily small. Two notions of density (natural and exponential density) are defined and some of their properties are studied. A class of subsets of the free group (graphical sets) is defined restricting the occurrence ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2001
ISSN: 1071-5797
DOI: 10.1006/ffta.2000.0284