Search Results for ""

A simple group is a group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group. Simple groups ...

According to the novel The Hitchhiker's Guide to the Galaxy (Adams 1997), 42 is the ultimate answer to life, the universe, and everything. Unfortunately, it is left as an ...

Let P be the set of prime ideals of a commutative ring A. Then an affine scheme is a technical mathematical object defined as the ring spectrum sigma(A) of P, regarded as a ...

Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N=a (mod r) (1) and N=b (mod s). (2) ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

The cross number of a zero-system sigma={g_1,g_2,...,g_n} of G is defined as K(sigma)=sum_(i=1)^n1/(|g_i|) The cross number of a group G has two different definitions. 1. ...

A number is said to be cubefree if its prime factorization contains no tripled factors. All primes are therefore trivially cubefree. The cubefree numbers are 1, 2, 3, 4, 5, ...

The cyclic group C_(11) is unique group of group order 11. An example is the integers modulo 11 under addition (Z_(11)). No modulo multiplication group is isomorphic to ...