coprime elements
11Merkle–Hellman knapsack cryptosystem — The Merkle–Hellman knapsack cryptosystem was one of the earliest public key cryptosystems invented by Ralph Merkle and Martin Hellman in 1978.[1] Although its ideas are elegant, and far simpler than RSA, it has been broken.[2] Contents 1… …
12Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …
13Euler's theorem — In number theory, Euler s theorem (also known as the Fermat Euler theorem or Euler s totient theorem) states that if n is a positive integer and a is coprime to n , then:a^{varphi (n)} equiv 1 pmod{n}where φ( n ) is Euler s totient function and …
14Abelian group — For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… …
15Abelian root group — If G is an abelian group and P is a set of primes then G is an abelian P root group if every element in G has a p th root for every prime p in P ::gin G,pin P Rightarrow exists hin G, h^p=g;(with the product written multiplicatively)If the set of …
16Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …
17Ideal (ring theory) — In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like even number or multiple of 3 . For instance, in… …
18Cyclic code — In coding theory, cyclic codes are linear block error correcting codes that have convenient algebraic structures for efficient error detection and correction. Contents 1 Definition 2 Algebraic structure 3 Examples …
19Focal subgroup theorem — In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in (Higman 1958) and is the first major application of the transfer according to… …
20Semidirect product — In mathematics, especially in the area of abstract algebra known as group theory, a semidirect product is a particular way in which a group can be put together from two subgroups, one of which is a normal subgroup. A semidirect product is a… …
