the binary cyclic group of the n-gon is the cyclic group of order 2n, C 2 n {\displaystyle C_{2n}} , thought of as an extension of the cyclic group C n...

extension of the cyclic group of order 2 by a cyclic group of order 2n, giving the name di-cyclic. In the notation of exact sequences of groups, this extension...

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...

3-sphere by the binary icosahedral group. binary polyhedral group binary cyclic group, ⟨n⟩, order 2n binary dihedral group, ⟨2,2,n⟩, order 4n binary tetrahedral...

that cyclically rotates i, j, and k. One can show that the binary tetrahedral group is isomorphic to the special linear group SL(2,3) – the group of all...

n {\displaystyle A_{n}} : binary cyclic group of an (n + 1)-gon, order 2n D n {\displaystyle D_{n}} : binary dihedral group of an n-gon, ⟨2,2,n⟩, order...

polyhedral group binary cyclic group, ⟨n⟩, index 2n binary dihedral group, ⟨2,2,n⟩, index 4n binary tetrahedral group, 2T=⟨2,3,3⟩, index 24 binary icosahedral...

information) and the algorithm is based on cyclic codes. CRCs are popular because they are simple to implement in binary hardware, easy to analyze mathematically...

the group within that order. Common group names: Zn: the cyclic group of order n (the notation Cn is also used; it is isomorphic to the additive group of...

code". Other names include "cyclic binary code", "cyclic progression code", "cyclic permuting binary" or "cyclic permuted binary" (CPB). The Gray code is...

four-group, with four elements, is the smallest group that is not cyclic. Up to isomorphism, there is only one other group of order four: the cyclic group...

A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the...

cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order is not modeled as a binary relation...

U1(H): the binary cyclic groups, binary dihedral groups, binary tetrahedral group, binary octahedral group, and binary icosahedral group. Hoggar, S.G...

out ∞.) As a cyclic code: The perfect G23 code can be constructed via the factorization of x 23 + 1 {\displaystyle x^{23}+1} over the binary field GF(2):...

the group structure (the rest of the structure is "factored out"). For example, the cyclic group of addition modulo n can be obtained from the group of...

(xxiv+835+1 pages) (NB. Ledley classified the described cyclic code as a cyclic decimal-coded binary code.) Savard, John J. G. (2018) [2006]. "Decimal Representations"...

there are essentially only 18 possibilities. One of these is C3, the cyclic group with three elements. The others all have a semigroup with two elements...

multiplication. In the case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication...

automorphism group Quotient group Examples of groups Abelian group Cyclic group Rank of an abelian group Dicyclic group Dihedral group Divisible group Finitely...

subgroup is cyclic) is either cyclic or a generalized quaternion group as defined above. Another characterization is that a finite p-group in which there...

is that an Archimedean group is a linearly ordered group without any bounded cyclic subgroups: there does not exist a cyclic subgroup S and an element...

a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary message...

{\displaystyle a^{-1}} ⁠. Formally, a group is an ordered pair of a set and a binary operation on this set that satisfies the group axioms. The set is called the...

3, and 3. The fundamental group is a product of a cyclic group of order m coprime to 6 with the binary octahedral group (of order 48) which has the...

subgroup is cyclic. Every cyclic group is locally cyclic, and every finitely-generated locally cyclic group is cyclic. Every locally cyclic group is abelian...

now usually presented as a group of automorphisms of the infinite regular binary rooted tree. The study of Grigorchuk's group informed in large part the...

definition is that a number n is cyclic if and only if any group of order n is cyclic. Any prime number is clearly cyclic. All cyclic numbers are square-free....

A pseudorandom binary sequence (PRBS), pseudorandom binary code or pseudorandom bitstream is a binary sequence that, while generated with a deterministic...

recreational mathematics concerning the reconstruction of necklaces (cyclic arrangements of binary values) from partial information. The necklace problem involves...