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In every residue class modulo p, there is exactly one integer polynomial with coefficients >=0 and <=p-1. This polynomial is called the normal polynomial modulo p in the ...

A normal series of a group G is a finite sequence (A_0,...,A_r) of normal subgroups such that I=A_0<|A_1<|...<|A_r=G.

The set of elements g of a group such that g^(-1)Hg=H, is said to be the normalizer N_G(H) with respect to a subset of group elements H. If H is a subgroup of G, N_G(H) is ...

Let K be a number field of extension degree d over Q. Then an order O of K is a subring of the ring of integers of K with d generators over Z, including 1. The ring of ...

The algebraic integers in a number field.

The letter O is used for a number of different purposes in mathematics. The double-struck O is sometimes used to represent octonions. The symbols O(x) (sometimes called the ...

The O'Nan group is the sporadic group O'N of order |O'N| = 460815505920 (1) = 2^9·3^4·5·7^3·11·19·31. (2) It is implemented in the Wolfram Language as ONanGroupON[].

The sum of the first n odd numbers is a square number, sum_(k=1)^n(2k-1)=n^2. A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is ...

A right or left ideal of a ring. The term is used especially in noncommutative rings to denote a right ideal that is not a left ideal, or conversely.

Two representations of a group chi_i and chi_j are said to be orthogonal if sum_(R)chi_i(R)chi_j(R)=0 for i!=j, where the sum is over all elements R of the representation.